Roundest Polyhedra

This is a collection of solutions and putative solutions to the Isoperimetric Problem for Polyhedra also know as Roundest Polyhedra with their faces tangent to a unit sphere. They have been rotated so that usually their primary axis of symmetry, if there is one, conincides with the Z-axis, and a second axis of symmetry is in the X-Z plane. In the case of C_s symmetry the reflective plane is made to coincide with the X-Z plane.

Each polyhedron is provided in two forms. The first, minvol.n.txt, is an unordered list of the tangent points of the faces in N. J. A. Sloane's future-proof format: each point's X, Y and Z coordinates are on three consecutive lines in the file. The second, minvol.n.off, in the simple OFF polyhedron file format. The first line is the literal "OFF". The second line is three space separated integers for the number of vertices, number of faces, and number of edges of the polyhedron. The next lines are the X, Y and Z coordinates of the polyhedron vertices. Finally are lines for each of the polyhedron faces, lists of space separated integers. The first on each line is the number of sides of the polygon, followed by that number of zero-based indices into the preceding list of vertices, in counter-clockwise order.

minimum volume polyhedron for n=4

proven best
volume: 13.856406460551, IQ: 0.302299894039, symmetry: T_d
face tanget points: minvol.4.txt polyhedron: minvol.4.off

minimum volume polyhedron for n=5

proven best
volume: 10.392304845413, IQ: 0.403066525385, symmetry: D_3h
face tanget points: minvol.5.txt polyhedron: minvol.5.off

minimum volume polyhedron for n=6

proven best
volume: 8.000000000000, IQ: 0.523598775598, symmetry: O_h
face tanget points: minvol.6.txt polyhedron: minvol.6.off

minimum volume polyhedron for n=7

incomplete proof of best by L. Lindelöf
volume: 7.265425280054, IQ: 0.576537510651, symmetry: D_5h
face tanget points: minvol.7.txt polyhedron: minvol.7.off

minimum volume polyhedron for n=8

M. Goldberg [1935]
volume: 6.700917103633, IQ: 0.625107002520, symmetry: D_2d
face tanget points: minvol.8.txt polyhedron: minvol.8.off

minimum volume polyhedron for n=9

M. Goldberg [1935]
volume: 6.263190158871, IQ: 0.668794990817, symmetry: D_3h
face tanget points: minvol.9.txt polyhedron: minvol.9.off

minimum volume polyhedron for n=10

M. Goldberg [1935]
volume: 5.974523836620, IQ: 0.701108627120, symmetry: D_4d
face tanget points: minvol.10.txt polyhedron: minvol.10.off

minimum volume polyhedron for n=11

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 5.779084247918, IQ: 0.724819024103, symmetry: C_2v
face tanget points: minvol.11.txt polyhedron: minvol.11.off

minimum volume polyhedron for n=12

proven best by M. Goldberg [1935]
volume: 5.550291028516, IQ: 0.754697399337, symmetry: I_h
face tanget points: minvol.12.txt polyhedron: minvol.12.off

minimum volume polyhedron for n=13

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 5.450567787592, IQ: 0.768505294865, symmetry: C_2v
face tanget points: minvol.13.txt polyhedron: minvol.13.off

minimum volume polyhedron for n=14

M. Goldberg [1935]
volume: 5.331297102787, IQ: 0.785698137625, symmetry: D_6d
face tanget points: minvol.14.txt polyhedron: minvol.14.off

minimum volume polyhedron for n=15

M. Goldberg [1935]
volume: 5.240415903349, IQ: 0.799324000622, symmetry: D_3h
face tanget points: minvol.15.txt polyhedron: minvol.15.off

minimum volume polyhedron for n=16

M. Goldberg [1935]
volume: 5.157407573326, IQ: 0.812189097959, symmetry: T_d
face tanget points: minvol.16.txt polyhedron: minvol.16.off

minimum volume polyhedron for n=17

M. Goldberg [1935]
volume: 5.094434009267, IQ: 0.822228769117, symmetry: C_2v
face tanget points: minvol.17.txt polyhedron: minvol.17.off

minimum volume polyhedron for n=18

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 5.034465113368, IQ: 0.832022888323, symmetry: D₃
face tanget points: minvol.18.txt polyhedron: minvol.18.off

minimum volume polyhedron for n=19

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.984573313752, IQ: 0.840350806604, symmetry: C₂
face tanget points: minvol.19.txt polyhedron: minvol.19.off

minimum volume polyhedron for n=20

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.935487080669, IQ: 0.848708574518, symmetry: D_2d
face tanget points: minvol.20.txt polyhedron: minvol.20.off

minimum volume polyhedron for n=21

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.894265461512, IQ: 0.855856764968, symmetry: C₂
face tanget points: minvol.21.txt polyhedron: minvol.21.off

minimum volume polyhedron for n=22

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.856963051173, IQ: 0.862429909524, symmetry: D₂
face tanget points: minvol.22.txt polyhedron: minvol.22.off

minimum volume polyhedron for n=23

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.824767875982, IQ: 0.868184814784, symmetry: D₃
face tanget points: minvol.23.txt polyhedron: minvol.23.off

minimum volume polyhedron for n=24

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.793509148243, IQ: 0.873846294071, symmetry: D₂
face tanget points: minvol.24.txt polyhedron: minvol.24.off

minimum volume polyhedron for n=25

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.767461826548, IQ: 0.878620607188, symmetry: C₁
face tanget points: minvol.25.txt polyhedron: minvol.25.off

minimum volume polyhedron for n=26

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.741701643780, IQ: 0.883393878289, symmetry: C₂
face tanget points: minvol.26.txt polyhedron: minvol.26.off

minimum volume polyhedron for n=27

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.717027125451, IQ: 0.888014864741, symmetry: D_5h
face tanget points: minvol.27.txt polyhedron: minvol.27.off

minimum volume polyhedron for n=28

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.696495963054, IQ: 0.891896903082, symmetry: T
face tanget points: minvol.28.txt polyhedron: minvol.28.off

minimum volume polyhedron for n=29

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.678488519055, IQ: 0.895329803146, symmetry: D₃
face tanget points: minvol.29.txt polyhedron: minvol.29.off

minimum volume polyhedron for n=30

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.660099339437, IQ: 0.898862856707, symmetry: C_2v
face tanget points: minvol.30.txt polyhedron: minvol.30.off

minimum volume polyhedron for n=31

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.642376448458, IQ: 0.902294385492, symmetry: C_3v
face tanget points: minvol.31.txt polyhedron: minvol.31.off

minimum volume polyhedron for n=32

M. Goldberg [1935]
volume: 4.624418470123, IQ: 0.905798260224, symmetry: I_h
face tanget points: minvol.32.txt polyhedron: minvol.32.off

minimum volume polyhedron for n=33

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.612996379070, IQ: 0.908041077984, symmetry: C_s
face tanget points: minvol.33.txt polyhedron: minvol.33.off

minimum volume polyhedron for n=34

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.599182176823, IQ: 0.910768489645, symmetry: D₂
face tanget points: minvol.34.txt polyhedron: minvol.34.off

minimum volume polyhedron for n=35

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.587014001206, IQ: 0.913184525638, symmetry: C_2v
face tanget points: minvol.35.txt polyhedron: minvol.35.off

minimum volume polyhedron for n=36

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.574833084287, IQ: 0.915615964039, symmetry: C_s
face tanget points: minvol.36.txt polyhedron: minvol.36.off

minimum volume polyhedron for n=37

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.562705367169, IQ: 0.918049680553, symmetry: D_5h
face tanget points: minvol.37.txt polyhedron: minvol.37.off

minimum volume polyhedron for n=38

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.552156206662, IQ: 0.920177167615, symmetry: C_2v
face tanget points: minvol.38.txt polyhedron: minvol.38.off

minimum volume polyhedron for n=39

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.541637872064, IQ: 0.922308277935, symmetry: D_3h
face tanget points: minvol.39.txt polyhedron: minvol.39.off

minimum volume polyhedron for n=40

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.532030503407, IQ: 0.924263462401, symmetry: T_d
face tanget points: minvol.40.txt polyhedron: minvol.40.off

minimum volume polyhedron for n=41

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.523153355092, IQ: 0.926077423413, symmetry: D_3h
face tanget points: minvol.41.txt polyhedron: minvol.41.off

minimum volume polyhedron for n=42

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.514652686824, IQ: 0.927821140486, symmetry: D_5h
face tanget points: minvol.42.txt polyhedron: minvol.42.off

minimum volume polyhedron for n=43

found in 1986 with Monte Carlo search by A. H. Schoen
volume: 4.506655880993, IQ: 0.929467506595, symmetry: C_2v
face tanget points: minvol.43.txt polyhedron: minvol.43.off

minimum volume polyhedron for n=44

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.498630986847, IQ: 0.931125539533, symmetry: D_2d
face tanget points: minvol.44.txt polyhedron: minvol.44.off

minimum volume polyhedron for n=45

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.491631962462, IQ: 0.932576453234, symmetry: C₂
face tanget points: minvol.45.txt polyhedron: minvol.45.off

minimum volume polyhedron for n=46

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.484925856677, IQ: 0.933970892417, symmetry: T
face tanget points: minvol.46.txt polyhedron: minvol.46.off

minimum volume polyhedron for n=47

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.478282932850, IQ: 0.935356311246, symmetry: C₂
face tanget points: minvol.47.txt polyhedron: minvol.47.off

minimum volume polyhedron for n=48

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.471311942045, IQ: 0.936814576813, symmetry: D₂
face tanget points: minvol.48.txt polyhedron: minvol.48.off

minimum volume polyhedron for n=49

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.465664169498, IQ: 0.937999376083, symmetry: C₃
face tanget points: minvol.49.txt polyhedron: minvol.49.off

minimum volume polyhedron for n=50

found in 2013 by T. Tarnai et al
volume: 4.459412031894, IQ: 0.939314460029, symmetry: D_6d
face tanget points: minvol.50.txt polyhedron: minvol.50.off

minimum volume polyhedron for n=51

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.453999620989, IQ: 0.940455896100, symmetry: D₃
face tanget points: minvol.51.txt polyhedron: minvol.51.off

minimum volume polyhedron for n=52

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.448721343537, IQ: 0.941571719450, symmetry: C₃
face tanget points: minvol.52.txt polyhedron: minvol.52.off

minimum volume polyhedron for n=53

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.443467240685, IQ: 0.942685065040, symmetry: C₂
face tanget points: minvol.53.txt polyhedron: minvol.53.off

minimum volume polyhedron for n=54

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.438483524544, IQ: 0.943743551513, symmetry: D₃
face tanget points: minvol.54.txt polyhedron: minvol.54.off

minimum volume polyhedron for n=55

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.433714086070, IQ: 0.944758756084, symmetry: C₂
face tanget points: minvol.55.txt polyhedron: minvol.55.off

minimum volume polyhedron for n=56

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.429149161107, IQ: 0.945732476469, symmetry: D₂
face tanget points: minvol.56.txt polyhedron: minvol.56.off

minimum volume polyhedron for n=57

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.424727466406, IQ: 0.946677560729, symmetry: C₂
face tanget points: minvol.57.txt polyhedron: minvol.57.off

minimum volume polyhedron for n=58

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.420443903619, IQ: 0.947594923975, symmetry: C₂
face tanget points: minvol.58.txt polyhedron: minvol.58.off

minimum volume polyhedron for n=59

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.416269382355, IQ: 0.948490647224, symmetry: C₂
face tanget points: minvol.59.txt polyhedron: minvol.59.off

minimum volume polyhedron for n=60

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.412092973028, IQ: 0.949388471728, symmetry: D₃
face tanget points: minvol.60.txt polyhedron: minvol.60.off

minimum volume polyhedron for n=61

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.408425349313, IQ: 0.950178322842, symmetry: C₂
face tanget points: minvol.61.txt polyhedron: minvol.61.off

minimum volume polyhedron for n=62

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.404677784343, IQ: 0.950986748605, symmetry: D₅
face tanget points: minvol.62.txt polyhedron: minvol.62.off

minimum volume polyhedron for n=63

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.401128756307, IQ: 0.951753615202, symmetry: C₂
face tanget points: minvol.63.txt polyhedron: minvol.63.off

minimum volume polyhedron for n=64

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.397580437772, IQ: 0.952521565906, symmetry: D₂
face tanget points: minvol.64.txt polyhedron: minvol.64.off

minimum volume polyhedron for n=65

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.394282399827, IQ: 0.953236461305, symmetry: C₂
face tanget points: minvol.65.txt polyhedron: minvol.65.off

minimum volume polyhedron for n=66

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.391032714213, IQ: 0.953941926060, symmetry: C₂
face tanget points: minvol.66.txt polyhedron: minvol.66.off

minimum volume polyhedron for n=67

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.387626174705, IQ: 0.954682563646, symmetry: D₅
face tanget points: minvol.67.txt polyhedron: minvol.67.off

minimum volume polyhedron for n=68

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.384709867970, IQ: 0.955317530901, symmetry: D₃
face tanget points: minvol.68.txt polyhedron: minvol.68.off

minimum volume polyhedron for n=69

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.381752143670, IQ: 0.955962379305, symmetry: D₃
face tanget points: minvol.69.txt polyhedron: minvol.69.off

minimum volume polyhedron for n=70

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.378845272438, IQ: 0.956596989428, symmetry: C₃
face tanget points: minvol.70.txt polyhedron: minvol.70.off

minimum volume polyhedron for n=71

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.376024057603, IQ: 0.957213705786, symmetry: C₂
face tanget points: minvol.71.txt polyhedron: minvol.71.off

minimum volume polyhedron for n=72

found in 2013 by T. Tarnai et al
volume: 4.372974589015, IQ: 0.957881213238, symmetry: I
face tanget points: minvol.72.txt polyhedron: minvol.72.off

minimum volume polyhedron for n=73

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.370695391702, IQ: 0.958380721919, symmetry: C₂
face tanget points: minvol.73.txt polyhedron: minvol.73.off

minimum volume polyhedron for n=74

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.368239224783, IQ: 0.958919598776, symmetry: C₂
face tanget points: minvol.74.txt polyhedron: minvol.74.off

minimum volume polyhedron for n=75

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.365657582301, IQ: 0.959486658268, symmetry: D₃
face tanget points: minvol.75.txt polyhedron: minvol.75.off

minimum volume polyhedron for n=76

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.363225434095, IQ: 0.960021495120, symmetry: C₂
face tanget points: minvol.76.txt polyhedron: minvol.76.off

minimum volume polyhedron for n=77

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.360694786381, IQ: 0.960578625651, symmetry: D₅
face tanget points: minvol.77.txt polyhedron: minvol.77.off

minimum volume polyhedron for n=78

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.358366011061, IQ: 0.961091884930, symmetry: T_h
face tanget points: minvol.78.txt polyhedron: minvol.78.off

minimum volume polyhedron for n=79

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.356250679514, IQ: 0.961558577078, symmetry: C₂
face tanget points: minvol.79.txt polyhedron: minvol.79.off

minimum volume polyhedron for n=80

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.354157562438, IQ: 0.962020814525, symmetry: D₂
face tanget points: minvol.80.txt polyhedron: minvol.80.off

minimum volume polyhedron for n=81

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.352108709281, IQ: 0.962473707482, symmetry: C₂
face tanget points: minvol.81.txt polyhedron: minvol.81.off

minimum volume polyhedron for n=82

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.350041156257, IQ: 0.962931166470, symmetry: C₂
face tanget points: minvol.82.txt polyhedron: minvol.82.off

minimum volume polyhedron for n=83

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.348016507592, IQ: 0.963379554211, symmetry: C₂
face tanget points: minvol.83.txt polyhedron: minvol.83.off

minimum volume polyhedron for n=84

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.346047235514, IQ: 0.963816078794, symmetry: D₂
face tanget points: minvol.84.txt polyhedron: minvol.84.off

minimum volume polyhedron for n=85

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.344109186640, IQ: 0.964246068600, symmetry: C₂
face tanget points: minvol.85.txt polyhedron: minvol.85.off

minimum volume polyhedron for n=86

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.342235850039, IQ: 0.964662065684, symmetry: D₃
face tanget points: minvol.86.txt polyhedron: minvol.86.off

minimum volume polyhedron for n=87

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.340408875936, IQ: 0.965068113285, symmetry: C₁
face tanget points: minvol.87.txt polyhedron: minvol.87.off

minimum volume polyhedron for n=88

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.338565314185, IQ: 0.965478194160, symmetry: D₂
face tanget points: minvol.88.txt polyhedron: minvol.88.off

minimum volume polyhedron for n=89

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.336834851610, IQ: 0.965863434535, symmetry: C₂
face tanget points: minvol.89.txt polyhedron: minvol.89.off

minimum volume polyhedron for n=90

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.335124107967, IQ: 0.966244587344, symmetry: D₃
face tanget points: minvol.90.txt polyhedron: minvol.90.off

minimum volume polyhedron for n=91

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.333462244237, IQ: 0.966615137897, symmetry: C₂
face tanget points: minvol.91.txt polyhedron: minvol.91.off

minimum volume polyhedron for n=92

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.331806941106, IQ: 0.966984508252, symmetry: D₂
face tanget points: minvol.92.txt polyhedron: minvol.92.off

minimum volume polyhedron for n=93

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.330271638273, IQ: 0.967327353731, symmetry: C₁
face tanget points: minvol.93.txt polyhedron: minvol.93.off

minimum volume polyhedron for n=94

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.328685219093, IQ: 0.967681869384, symmetry: D₂
face tanget points: minvol.94.txt polyhedron: minvol.94.off

minimum volume polyhedron for n=95

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.327175830239, IQ: 0.968019412457, symmetry: C₂
face tanget points: minvol.95.txt polyhedron: minvol.95.off

minimum volume polyhedron for n=96

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.325693746611, IQ: 0.968351078499, symmetry: C₁
face tanget points: minvol.96.txt polyhedron: minvol.96.off

minimum volume polyhedron for n=97

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.324244282049, IQ: 0.968675664827, symmetry: C₂
face tanget points: minvol.97.txt polyhedron: minvol.97.off

minimum volume polyhedron for n=98

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.322782203400, IQ: 0.969003296417, symmetry: D₃
face tanget points: minvol.98.txt polyhedron: minvol.98.off

minimum volume polyhedron for n=99

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.321426194818, IQ: 0.969307357328, symmetry: C₁
face tanget points: minvol.99.txt polyhedron: minvol.99.off

minimum volume polyhedron for n=100

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.320055397679, IQ: 0.969614928326, symmetry: D₂
face tanget points: minvol.100.txt polyhedron: minvol.100.off

minimum volume polyhedron for n=101

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.318725982098, IQ: 0.969913400885, symmetry: D₃
face tanget points: minvol.101.txt polyhedron: minvol.101.off

minimum volume polyhedron for n=102

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.317432089125, IQ: 0.970204074625, symmetry: D₃
face tanget points: minvol.102.txt polyhedron: minvol.102.off

minimum volume polyhedron for n=103

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.316137133323, IQ: 0.970495161622, symmetry: C₂
face tanget points: minvol.103.txt polyhedron: minvol.103.off

minimum volume polyhedron for n=104

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.314866888625, IQ: 0.970780863676, symmetry: D₂
face tanget points: minvol.104.txt polyhedron: minvol.104.off

minimum volume polyhedron for n=105

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.313656203665, IQ: 0.971053326231, symmetry: D₃
face tanget points: minvol.105.txt polyhedron: minvol.105.off

minimum volume polyhedron for n=106

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.312454749167, IQ: 0.971323862725, symmetry: D₂
face tanget points: minvol.106.txt polyhedron: minvol.106.off

minimum volume polyhedron for n=107

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.311249410606, IQ: 0.971595425327, symmetry: C₂
face tanget points: minvol.107.txt polyhedron: minvol.107.off

minimum volume polyhedron for n=108

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.310056562017, IQ: 0.971864323476, symmetry: C₂
face tanget points: minvol.108.txt polyhedron: minvol.108.off

minimum volume polyhedron for n=109

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.308941371905, IQ: 0.972115850101, symmetry: C₂
face tanget points: minvol.109.txt polyhedron: minvol.109.off

minimum volume polyhedron for n=110

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.307799846405, IQ: 0.972373451446, symmetry: C₂
face tanget points: minvol.110.txt polyhedron: minvol.110.off

minimum volume polyhedron for n=111

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.306652870593, IQ: 0.972632420270, symmetry: D₃
face tanget points: minvol.111.txt polyhedron: minvol.111.off

minimum volume polyhedron for n=112

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.305579058739, IQ: 0.972874994894, symmetry: T
face tanget points: minvol.112.txt polyhedron: minvol.112.off

minimum volume polyhedron for n=113

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.304545690266, IQ: 0.973108547613, symmetry: D₃
face tanget points: minvol.113.txt polyhedron: minvol.113.off

minimum volume polyhedron for n=114

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.303516795996, IQ: 0.973341200546, symmetry: C₂
face tanget points: minvol.114.txt polyhedron: minvol.114.off

minimum volume polyhedron for n=115

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.302498193289, IQ: 0.973571635967, symmetry: C₃
face tanget points: minvol.115.txt polyhedron: minvol.115.off

minimum volume polyhedron for n=116

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.301496629966, IQ: 0.973798323032, symmetry: T_d
face tanget points: minvol.116.txt polyhedron: minvol.116.off

minimum volume polyhedron for n=117

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.300516651404, IQ: 0.974020226946, symmetry: C₂
face tanget points: minvol.117.txt polyhedron: minvol.117.off

minimum volume polyhedron for n=118

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.299552693537, IQ: 0.974238601863, symmetry: C₂
face tanget points: minvol.118.txt polyhedron: minvol.118.off

minimum volume polyhedron for n=119

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.298563284743, IQ: 0.974462844284, symmetry: D_3h
face tanget points: minvol.119.txt polyhedron: minvol.119.off

minimum volume polyhedron for n=120

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.297629946251, IQ: 0.974674473413, symmetry: C₁
face tanget points: minvol.120.txt polyhedron: minvol.120.off

minimum volume polyhedron for n=121

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.296662021449, IQ: 0.974894041904, symmetry: C₃
face tanget points: minvol.121.txt polyhedron: minvol.121.off

minimum volume polyhedron for n=122

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.295676863313, IQ: 0.975117621291, symmetry: I_h
face tanget points: minvol.122.txt polyhedron: minvol.122.off

minimum volume polyhedron for n=123

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.294893998828, IQ: 0.975295363734, symmetry: C₂
face tanget points: minvol.123.txt polyhedron: minvol.123.off

minimum volume polyhedron for n=124

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.294038669989, IQ: 0.975489632653, symmetry: D₂
face tanget points: minvol.124.txt polyhedron: minvol.124.off

minimum volume polyhedron for n=125

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.293173600019, IQ: 0.975686192789, symmetry: C_2v
face tanget points: minvol.125.txt polyhedron: minvol.125.off

minimum volume polyhedron for n=126

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.292340657164, IQ: 0.975875527912, symmetry: D₃
face tanget points: minvol.126.txt polyhedron: minvol.126.off

minimum volume polyhedron for n=127

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.291464861598, IQ: 0.976074683092, symmetry: D₅
face tanget points: minvol.127.txt polyhedron: minvol.127.off

minimum volume polyhedron for n=128

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.290666421792, IQ: 0.976256318485, symmetry: C₂
face tanget points: minvol.128.txt polyhedron: minvol.128.off

minimum volume polyhedron for n=129

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.289849504225, IQ: 0.976442227323, symmetry: C₂
face tanget points: minvol.129.txt polyhedron: minvol.129.off

minimum volume polyhedron for n=130

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.289056928886, IQ: 0.976622664198, symmetry: C₂
face tanget points: minvol.130.txt polyhedron: minvol.130.off

minimum volume polyhedron for n=131

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.288271337055, IQ: 0.976801577034, symmetry: C₂
face tanget points: minvol.131.txt polyhedron: minvol.131.off

minimum volume polyhedron for n=132

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.287430162420, IQ: 0.976993221138, symmetry: I
face tanget points: minvol.132.txt polyhedron: minvol.132.off

minimum volume polyhedron for n=133

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.286725909074, IQ: 0.977153728425, symmetry: C₃
face tanget points: minvol.133.txt polyhedron: minvol.133.off

minimum volume polyhedron for n=134

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.285970996386, IQ: 0.977325840123, symmetry: C₂
face tanget points: minvol.134.txt polyhedron: minvol.134.off

minimum volume polyhedron for n=135

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.285206288725, IQ: 0.977500246793, symmetry: D₃
face tanget points: minvol.135.txt polyhedron: minvol.135.off

minimum volume polyhedron for n=136

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.284472873691, IQ: 0.977667575049, symmetry: T
face tanget points: minvol.136.txt polyhedron: minvol.136.off

minimum volume polyhedron for n=137

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.283759097183, IQ: 0.977830477802, symmetry: D₃
face tanget points: minvol.137.txt polyhedron: minvol.137.off

minimum volume polyhedron for n=138

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.283083012137, IQ: 0.977984828432, symmetry: C₂
face tanget points: minvol.138.txt polyhedron: minvol.138.off

minimum volume polyhedron for n=139

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.282412684627, IQ: 0.978137912729, symmetry: C₂
face tanget points: minvol.139.txt polyhedron: minvol.139.off

minimum volume polyhedron for n=140

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.281753245126, IQ: 0.978288557276, symmetry: C₁
face tanget points: minvol.140.txt polyhedron: minvol.140.off

minimum volume polyhedron for n=141

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.281060508882, IQ: 0.978446858225, symmetry: C_2v
face tanget points: minvol.141.txt polyhedron: minvol.141.off

minimum volume polyhedron for n=142

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.280391864417, IQ: 0.978599702426, symmetry: C₂
face tanget points: minvol.142.txt polyhedron: minvol.142.off

minimum volume polyhedron for n=143

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.279724426684, IQ: 0.978752318413, symmetry: C₂
face tanget points: minvol.143.txt polyhedron: minvol.143.off

minimum volume polyhedron for n=144

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.279068729136, IQ: 0.978902296256, symmetry: C₂
face tanget points: minvol.144.txt polyhedron: minvol.144.off

minimum volume polyhedron for n=145

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.278429607731, IQ: 0.979048526875, symmetry: C_s
face tanget points: minvol.145.txt polyhedron: minvol.145.off

minimum volume polyhedron for n=146

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.277788512853, IQ: 0.979195252921, symmetry: D₂
face tanget points: minvol.146.txt polyhedron: minvol.146.off

minimum volume polyhedron for n=147

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.277202670192, IQ: 0.979329371970, symmetry: C₂
face tanget points: minvol.147.txt polyhedron: minvol.147.off

minimum volume polyhedron for n=148

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.276595106150, IQ: 0.979468502586, symmetry: C₂
face tanget points: minvol.148.txt polyhedron: minvol.148.off

minimum volume polyhedron for n=149

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.276023026802, IQ: 0.979599543438, symmetry: C₁
face tanget points: minvol.149.txt polyhedron: minvol.149.off

minimum volume polyhedron for n=150

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.275409687197, IQ: 0.979740074344, symmetry: T
face tanget points: minvol.150.txt polyhedron: minvol.150.off

minimum volume polyhedron for n=151

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.274831858269, IQ: 0.979872505788, symmetry: C₂
face tanget points: minvol.151.txt polyhedron: minvol.151.off

minimum volume polyhedron for n=152

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.274255875929, IQ: 0.980004549652, symmetry: D₂
face tanget points: minvol.152.txt polyhedron: minvol.152.off

minimum volume polyhedron for n=153

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.273668624475, IQ: 0.980139213602, symmetry: D₃
face tanget points: minvol.153.txt polyhedron: minvol.153.off

minimum volume polyhedron for n=154

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.273122350460, IQ: 0.980264514152, symmetry: C₂
face tanget points: minvol.154.txt polyhedron: minvol.154.off

minimum volume polyhedron for n=155

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.272565480821, IQ: 0.980392278033, symmetry: C₂
face tanget points: minvol.155.txt polyhedron: minvol.155.off

minimum volume polyhedron for n=156

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.272013815531, IQ: 0.980518880711, symmetry: D₃
face tanget points: minvol.156.txt polyhedron: minvol.156.off

minimum volume polyhedron for n=157

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.271473152712, IQ: 0.980642990142, symmetry: C₂
face tanget points: minvol.157.txt polyhedron: minvol.157.off

minimum volume polyhedron for n=158

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.270939182083, IQ: 0.980765594219, symmetry: C₂
face tanget points: minvol.158.txt polyhedron: minvol.158.off

minimum volume polyhedron for n=159

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.270398221643, IQ: 0.980889834479, symmetry: C₂
face tanget points: minvol.159.txt polyhedron: minvol.159.off

minimum volume polyhedron for n=160

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.269875252858, IQ: 0.981009972594, symmetry: D₂
face tanget points: minvol.160.txt polyhedron: minvol.160.off

minimum volume polyhedron for n=161

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.269366434318, IQ: 0.981126888317, symmetry: C₂
face tanget points: minvol.161.txt polyhedron: minvol.161.off

minimum volume polyhedron for n=162

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.268858678264, IQ: 0.981243587687, symmetry: D₃
face tanget points: minvol.162.txt polyhedron: minvol.162.off

minimum volume polyhedron for n=163

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.268362745398, IQ: 0.981357596494, symmetry: C₂
face tanget points: minvol.163.txt polyhedron: minvol.163.off

minimum volume polyhedron for n=164

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.267867687896, IQ: 0.981471430491, symmetry: C₂
face tanget points: minvol.164.txt polyhedron: minvol.164.off

minimum volume polyhedron for n=165

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.267378067552, IQ: 0.981584040242, symmetry: C₂
face tanget points: minvol.165.txt polyhedron: minvol.165.off

minimum volume polyhedron for n=166

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.266898904442, IQ: 0.981694269912, symmetry: C₂
face tanget points: minvol.166.txt polyhedron: minvol.166.off

minimum volume polyhedron for n=167

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.266426018593, IQ: 0.981803079798, symmetry: C₂
face tanget points: minvol.167.txt polyhedron: minvol.167.off

minimum volume polyhedron for n=168

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.265945568211, IQ: 0.981913654970, symmetry: D₃
face tanget points: minvol.168.txt polyhedron: minvol.168.off

minimum volume polyhedron for n=169

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.265500566166, IQ: 0.982016093964, symmetry: C₁
face tanget points: minvol.169.txt polyhedron: minvol.169.off

minimum volume polyhedron for n=170

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.265032108385, IQ: 0.982123955539, symmetry: C₂
face tanget points: minvol.170.txt polyhedron: minvol.170.off

minimum volume polyhedron for n=171

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.264578115328, IQ: 0.982228509247, symmetry: C₃
face tanget points: minvol.171.txt polyhedron: minvol.171.off

minimum volume polyhedron for n=172

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.264126408003, IQ: 0.982332558651, symmetry: C₂
face tanget points: minvol.172.txt polyhedron: minvol.172.off

minimum volume polyhedron for n=173

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.263679942062, IQ: 0.982435422383, symmetry: C_s
face tanget points: minvol.173.txt polyhedron: minvol.173.off

minimum volume polyhedron for n=174

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.263225115110, IQ: 0.982540234608, symmetry: T_h
face tanget points: minvol.174.txt polyhedron: minvol.174.off

minimum volume polyhedron for n=175

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.262813389407, IQ: 0.982635133688, symmetry: C₁
face tanget points: minvol.175.txt polyhedron: minvol.175.off

minimum volume polyhedron for n=176

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.262389672421, IQ: 0.982732815793, symmetry: C₂
face tanget points: minvol.176.txt polyhedron: minvol.176.off

minimum volume polyhedron for n=177

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.261964200561, IQ: 0.982830922004, symmetry: D₅
face tanget points: minvol.177.txt polyhedron: minvol.177.off

minimum volume polyhedron for n=178

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.261557948220, IQ: 0.982924614820, symmetry: C₂
face tanget points: minvol.178.txt polyhedron: minvol.178.off

minimum volume polyhedron for n=179

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.261149059783, IQ: 0.983018933630, symmetry: C₂
face tanget points: minvol.179.txt polyhedron: minvol.179.off

minimum volume polyhedron for n=180

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.260728898811, IQ: 0.983115871548, symmetry: C₂
face tanget points: minvol.180.txt polyhedron: minvol.180.off

minimum volume polyhedron for n=181

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.260317967368, IQ: 0.983210698561, symmetry: C₂
face tanget points: minvol.181.txt polyhedron: minvol.181.off

minimum volume polyhedron for n=182

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.259899519954, IQ: 0.983307278767, symmetry: D₅
face tanget points: minvol.182.txt polyhedron: minvol.182.off

minimum volume polyhedron for n=183

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.259526188459, IQ: 0.983393461962, symmetry: C₁
face tanget points: minvol.183.txt polyhedron: minvol.183.off

minimum volume polyhedron for n=184

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.259123986785, IQ: 0.983486326715, symmetry: T
face tanget points: minvol.184.txt polyhedron: minvol.184.off

minimum volume polyhedron for n=185

found in 2021 from best known minimum energy configuration by W. R. Deeter
volume: 4.258757075775, IQ: 0.983571058470, symmetry: C₂
face tanget points: minvol.185.txt polyhedron: minvol.185.off

minimum volume polyhedron for n=186

found in 2016 with constrained search by W. R. Deeter
volume: 4.258369057100, IQ: 0.983660680561, symmetry: D₃
face tanget points: minvol.186.txt polyhedron: minvol.186.off

minimum volume polyhedron for n=187

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.257963721367, IQ: 0.983754319880, symmetry: D₅
face tanget points: minvol.187.txt polyhedron: minvol.187.off

minimum volume polyhedron for n=188

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.257605084191, IQ: 0.983837185919, symmetry: D₂
face tanget points: minvol.188.txt polyhedron: minvol.188.off

minimum volume polyhedron for n=189

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.257237270258, IQ: 0.983922186825, symmetry: C₁
face tanget points: minvol.189.txt polyhedron: minvol.189.off

minimum volume polyhedron for n=190

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.256862197515, IQ: 0.984008880351, symmetry: C₃
face tanget points: minvol.190.txt polyhedron: minvol.190.off

minimum volume polyhedron for n=191

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.256498541619, IQ: 0.984092949599, symmetry: C₁
face tanget points: minvol.191.txt polyhedron: minvol.191.off

minimum volume polyhedron for n=192

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.256108030862, IQ: 0.984183243097, symmetry: I
face tanget points: minvol.192.txt polyhedron: minvol.192.off

minimum volume polyhedron for n=193

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.255795951700, IQ: 0.984255413635, symmetry: C₂
face tanget points: minvol.193.txt polyhedron: minvol.193.off

minimum volume polyhedron for n=194

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.255453145948, IQ: 0.984334702116, symmetry: C₂
face tanget points: minvol.194.txt polyhedron: minvol.194.off

minimum volume polyhedron for n=195

found in 2016 with constrained search by W. R. Deeter
volume: 4.255098220596, IQ: 0.984416807234, symmetry: D₃
face tanget points: minvol.195.txt polyhedron: minvol.195.off

minimum volume polyhedron for n=196

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.254758357734, IQ: 0.984495440775, symmetry: C₁
face tanget points: minvol.196.txt polyhedron: minvol.196.off

minimum volume polyhedron for n=197

found in 2016 with constrained search by W. R. Deeter
volume: 4.254402155575, IQ: 0.984577868196, symmetry: D₅
face tanget points: minvol.197.txt polyhedron: minvol.197.off

minimum volume polyhedron for n=198

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.254091732379, IQ: 0.984649713335, symmetry: D₃
face tanget points: minvol.198.txt polyhedron: minvol.198.off

minimum volume polyhedron for n=199

found in 2016 with constrained search by W. R. Deeter
volume: 4.253761308626, IQ: 0.984726198974, symmetry: C₂
face tanget points: minvol.199.txt polyhedron: minvol.199.off

minimum volume polyhedron for n=200

found in 2015 with Monte Carlo search by W. R. Deeter
volume: 4.253423192226, IQ: 0.984804477589, symmetry: C₁
face tanget points: minvol.200.txt polyhedron: minvol.200.off

minimum volume polyhedron for n=201

found in 2016 with constrained search by W. R. Deeter
volume: 4.253093120370, IQ: 0.984880905787, symmetry: C₁
face tanget points: minvol.201.txt polyhedron: minvol.201.off

minimum volume polyhedron for n=202

found in 2016 with constrained search by W. R. Deeter
volume: 4.252747197008, IQ: 0.984961017136, symmetry: D₅
face tanget points: minvol.202.txt polyhedron: minvol.202.off

minimum volume polyhedron for n=203

found in 2016 with constrained search by W. R. Deeter
volume: 4.252439342773, IQ: 0.985032323131, symmetry: C₁
face tanget points: minvol.203.txt polyhedron: minvol.203.off

minimum volume polyhedron for n=204

found in 2016 with constrained search by W. R. Deeter
volume: 4.252100370726, IQ: 0.985110848658, symmetry: T_h
face tanget points: minvol.204.txt polyhedron: minvol.204.off

minimum volume polyhedron for n=205

found in 2016 with constrained search by W. R. Deeter
volume: 4.251814044392, IQ: 0.985177188149, symmetry: C₁
face tanget points: minvol.205.txt polyhedron: minvol.205.off

minimum volume polyhedron for n=206

found in 2016 with constrained search by W. R. Deeter
volume: 4.251497988190, IQ: 0.985250426184, symmetry: C₂
face tanget points: minvol.206.txt polyhedron: minvol.206.off

minimum volume polyhedron for n=207

found in 2016 with constrained search by W. R. Deeter
volume: 4.251197639916, IQ: 0.985320034396, symmetry: D₅
face tanget points: minvol.207.txt polyhedron: minvol.207.off

minimum volume polyhedron for n=208

found in 2016 with constrained search by W. R. Deeter
volume: 4.250896047556, IQ: 0.985389940833, symmetry: C₂
face tanget points: minvol.208.txt polyhedron: minvol.208.off

minimum volume polyhedron for n=209

found in 2016 with constrained search by W. R. Deeter
volume: 4.250601480268, IQ: 0.985458228496, symmetry: C₂
face tanget points: minvol.209.txt polyhedron: minvol.209.off

minimum volume polyhedron for n=210

found in 2016 with constrained search by W. R. Deeter
volume: 4.250293492379, IQ: 0.985529637494, symmetry: C₂
face tanget points: minvol.210.txt polyhedron: minvol.210.off

minimum volume polyhedron for n=211

found in 2016 with constrained search by W. R. Deeter
volume: 4.250002631995, IQ: 0.985597084871, symmetry: C₁
face tanget points: minvol.211.txt polyhedron: minvol.211.off

minimum volume polyhedron for n=212

found in 2016 with constrained search by W. R. Deeter
volume: 4.249687998752, IQ: 0.985670055311, symmetry: I
face tanget points: minvol.212.txt polyhedron: minvol.212.off

minimum volume polyhedron for n=213

found in 2016 with constrained search by W. R. Deeter
volume: 4.249416137931, IQ: 0.985733114579, symmetry: C₁
face tanget points: minvol.213.txt polyhedron: minvol.213.off

minimum volume polyhedron for n=214

found in 2016 with constrained search by W. R. Deeter
volume: 4.249112271595, IQ: 0.985803607212, symmetry: T
face tanget points: minvol.214.txt polyhedron: minvol.214.off

minimum volume polyhedron for n=215

found in 2016 with constrained search by W. R. Deeter
volume: 4.248842166914, IQ: 0.985866276089, symmetry: C₁
face tanget points: minvol.215.txt polyhedron: minvol.215.off

minimum volume polyhedron for n=216

found in 2016 with constrained search by W. R. Deeter
volume: 4.248545851596, IQ: 0.985935035446, symmetry: D₃
face tanget points: minvol.216.txt polyhedron: minvol.216.off

minimum volume polyhedron for n=217

found in 2016 with constrained search by W. R. Deeter
volume: 4.248264282262, IQ: 0.986000381915, symmetry: D₅
face tanget points: minvol.217.txt polyhedron: minvol.217.off

minimum volume polyhedron for n=218

found in 2016 with constrained search by W. R. Deeter
volume: 4.248001354047, IQ: 0.986061409984, symmetry: C₂
face tanget points: minvol.218.txt polyhedron: minvol.218.off

minimum volume polyhedron for n=219

found in 2016 with constrained search by W. R. Deeter
volume: 4.247722901349, IQ: 0.986126049667, symmetry: C₂
face tanget points: minvol.219.txt polyhedron: minvol.219.off

minimum volume polyhedron for n=220

found in 2016 with constrained search by W. R. Deeter
volume: 4.247443455215, IQ: 0.986190928485, symmetry: D₂
face tanget points: minvol.220.txt polyhedron: minvol.220.off

minimum volume polyhedron for n=221

found in 2016 with constrained search by W. R. Deeter
volume: 4.247178361167, IQ: 0.986252483080, symmetry: C₂
face tanget points: minvol.221.txt polyhedron: minvol.221.off

minimum volume polyhedron for n=222

found in 2016 with constrained search by W. R. Deeter
volume: 4.246909804303, IQ: 0.986314849574, symmetry: D₃
face tanget points: minvol.222.txt polyhedron: minvol.222.off

minimum volume polyhedron for n=223

found in 2016 with constrained search by W. R. Deeter
volume: 4.246645225851, IQ: 0.986376299882, symmetry: C₂
face tanget points: minvol.223.txt polyhedron: minvol.223.off

minimum volume polyhedron for n=224

found in 2016 with constrained search by W. R. Deeter
volume: 4.246379504721, IQ: 0.986438023292, symmetry: D₂
face tanget points: minvol.224.txt polyhedron: minvol.224.off

minimum volume polyhedron for n=225

found in 2016 with constrained search by W. R. Deeter
volume: 4.246133172863, IQ: 0.986495249738, symmetry: C₁
face tanget points: minvol.225.txt polyhedron: minvol.225.off

minimum volume polyhedron for n=226

found in 2016 with constrained search by W. R. Deeter
volume: 4.245878234728, IQ: 0.986554482539, symmetry: C₃
face tanget points: minvol.226.txt polyhedron: minvol.226.off

minimum volume polyhedron for n=227

found in 2016 with constrained search by W. R. Deeter
volume: 4.245624887997, IQ: 0.986613352637, symmetry: C₂
face tanget points: minvol.227.txt polyhedron: minvol.227.off

minimum volume polyhedron for n=228

found in 2021 with constrained search by W. R. Deeter
volume: 4.245372914428, IQ: 0.986671910623, symmetry: C₁
face tanget points: minvol.228.txt polyhedron: minvol.228.off

minimum volume polyhedron for n=229

found in 2021 with constrained search by W. R. Deeter
volume: 4.245122070515, IQ: 0.986730212984, symmetry: C₂
face tanget points: minvol.229.txt polyhedron: minvol.229.off

minimum volume polyhedron for n=230

found in 2016 with constrained search by W. R. Deeter
volume: 4.244873627833, IQ: 0.986787964033, symmetry: C₂
face tanget points: minvol.230.txt polyhedron: minvol.230.off

minimum volume polyhedron for n=231

found in 2016 with constrained search by W. R. Deeter
volume: 4.244623911287, IQ: 0.986846018006, symmetry: C₂
face tanget points: minvol.231.txt polyhedron: minvol.231.off

minimum volume polyhedron for n=232

found in 2021 with constrained search by W. R. Deeter
volume: 4.244382880277, IQ: 0.986902059248, symmetry: C₁
face tanget points: minvol.232.txt polyhedron: minvol.232.off

minimum volume polyhedron for n=233

found in 2016 with constrained search by W. R. Deeter
volume: 4.244132082643, IQ: 0.986960378052, symmetry: D₃
face tanget points: minvol.233.txt polyhedron: minvol.233.off

minimum volume polyhedron for n=234

found in 2016 with constrained search by W. R. Deeter
volume: 4.243893950746, IQ: 0.987015758028, symmetry: C₂
face tanget points: minvol.234.txt polyhedron: minvol.234.off

minimum volume polyhedron for n=235

found in 2016 with constrained search by W. R. Deeter
volume: 4.243656878313, IQ: 0.987070897789, symmetry: C₁
face tanget points: minvol.235.txt polyhedron: minvol.235.off

minimum volume polyhedron for n=236

found in 2016 with constrained search by W. R. Deeter
volume: 4.243415887396, IQ: 0.987126955250, symmetry: C₂
face tanget points: minvol.236.txt polyhedron: minvol.236.off

minimum volume polyhedron for n=237

found in 2016 with constrained search by W. R. Deeter
volume: 4.243191488437, IQ: 0.987179158942, symmetry: C₁
face tanget points: minvol.237.txt polyhedron: minvol.237.off

minimum volume polyhedron for n=238

found in 2016 with constrained search by W. R. Deeter
volume: 4.242962106723, IQ: 0.987232527519, symmetry: C₂
face tanget points: minvol.238.txt polyhedron: minvol.238.off

minimum volume polyhedron for n=239

found in 2016 with constrained search by W. R. Deeter
volume: 4.242734280136, IQ: 0.987285539987, symmetry: C₁
face tanget points: minvol.239.txt polyhedron: minvol.239.off

minimum volume polyhedron for n=240

found in 2016 with constrained search by W. R. Deeter
volume: 4.242506545897, IQ: 0.987338536658, symmetry: C₂
face tanget points: minvol.240.txt polyhedron: minvol.240.off

minimum volume polyhedron for n=241

found in 2016 with constrained search by W. R. Deeter
volume: 4.242280959674, IQ: 0.987391039067, symmetry: C₃
face tanget points: minvol.241.txt polyhedron: minvol.241.off

minimum volume polyhedron for n=242

found in 2016 with constrained search by W. R. Deeter
volume: 4.242053118010, IQ: 0.987444072070, symmetry: D₂
face tanget points: minvol.242.txt polyhedron: minvol.242.off

minimum volume polyhedron for n=243

found in 2016 with constrained search by W. R. Deeter
volume: 4.241832979263, IQ: 0.987495317535, symmetry: C₂
face tanget points: minvol.243.txt polyhedron: minvol.243.off

minimum volume polyhedron for n=244

found in 2016 with constrained search by W. R. Deeter
volume: 4.241612147916, IQ: 0.987546729572, symmetry: D₂
face tanget points: minvol.244.txt polyhedron: minvol.244.off

minimum volume polyhedron for n=245

found in 2016 with constrained search by W. R. Deeter
volume: 4.241400649558, IQ: 0.987595973802, symmetry: C₁
face tanget points: minvol.245.txt polyhedron: minvol.245.off

minimum volume polyhedron for n=246

found in 2016 with constrained search by W. R. Deeter
volume: 4.241176946324, IQ: 0.987648065101, symmetry: D₃
face tanget points: minvol.246.txt polyhedron: minvol.246.off

minimum volume polyhedron for n=247

found in 2016 with constrained search by W. R. Deeter
volume: 4.240968225048, IQ: 0.987696672672, symmetry: C₂
face tanget points: minvol.247.txt polyhedron: minvol.247.off

minimum volume polyhedron for n=248

found in 2016 with constrained search by W. R. Deeter
volume: 4.240752251899, IQ: 0.987746974115, symmetry: C₂
face tanget points: minvol.248.txt polyhedron: minvol.248.off

minimum volume polyhedron for n=249

found in 2016 with constrained search by W. R. Deeter
volume: 4.240541307913, IQ: 0.987796109183, symmetry: C₂
face tanget points: minvol.249.txt polyhedron: minvol.249.off

minimum volume polyhedron for n=250

found in 2016 with constrained search by W. R. Deeter
volume: 4.240330243295, IQ: 0.987845277242, symmetry: C₂
face tanget points: minvol.250.txt polyhedron: minvol.250.off

minimum volume polyhedron for n=251

found in 2016 with constrained search by W. R. Deeter
volume: 4.240122247657, IQ: 0.987893735163, symmetry: C₁
face tanget points: minvol.251.txt polyhedron: minvol.251.off

minimum volume polyhedron for n=252

found in 2016 with constrained search by W. R. Deeter
volume: 4.239909340119, IQ: 0.987943342361, symmetry: C₂
face tanget points: minvol.252.txt polyhedron: minvol.252.off

minimum volume polyhedron for n=253

found in 2016 with constrained search by W. R. Deeter
volume: 4.239709279260, IQ: 0.987989960839, symmetry: C₁
face tanget points: minvol.253.txt polyhedron: minvol.253.off

minimum volume polyhedron for n=254

found in 2016 with constrained search by W. R. Deeter
volume: 4.239503743723, IQ: 0.988037859617, symmetry: C₂
face tanget points: minvol.254.txt polyhedron: minvol.254.off

minimum volume polyhedron for n=255

found in 2016 with constrained search by W. R. Deeter
volume: 4.239294867176, IQ: 0.988086541755, symmetry: D₃
face tanget points: minvol.255.txt polyhedron: minvol.255.off

minimum volume polyhedron for n=256

found in 2016 with constrained search by W. R. Deeter
volume: 4.239095716411, IQ: 0.988132961605, symmetry: T
face tanget points: minvol.256.txt polyhedron: minvol.256.off

minimum volume polyhedron for n=257

found in 2016 with constrained search by W. R. Deeter
volume: 4.238901181520, IQ: 0.988178309758, symmetry: D₅
face tanget points: minvol.257.txt polyhedron: minvol.257.off

minimum volume polyhedron for n=258

found in 2016 with constrained search by W. R. Deeter
volume: 4.238709271119, IQ: 0.988223050193, symmetry: C₂
face tanget points: minvol.258.txt polyhedron: minvol.258.off

minimum volume polyhedron for n=259

found in 2016 with constrained search by W. R. Deeter
volume: 4.238516273309, IQ: 0.988268048223, symmetry: C₂
face tanget points: minvol.259.txt polyhedron: minvol.259.off

minimum volume polyhedron for n=260

found in 2016 with constrained search by W. R. Deeter
volume: 4.238320828948, IQ: 0.988313620851, symmetry: C₂
face tanget points: minvol.260.txt polyhedron: minvol.260.off

minimum volume polyhedron for n=261

found in 2016 with constrained search by W. R. Deeter
volume: 4.238133052666, IQ: 0.988357409438, symmetry: C₁
face tanget points: minvol.261.txt polyhedron: minvol.261.off

minimum volume polyhedron for n=262

found in 2016 with constrained search by W. R. Deeter
volume: 4.237944040402, IQ: 0.988401490169, symmetry: C₂
face tanget points: minvol.262.txt polyhedron: minvol.262.off

minimum volume polyhedron for n=263

found in 2016 with constrained search by W. R. Deeter
volume: 4.237756316957, IQ: 0.988445274219, symmetry: C₁
face tanget points: minvol.263.txt polyhedron: minvol.263.off

minimum volume polyhedron for n=264

found in 2016 with constrained search by W. R. Deeter
volume: 4.237561737513, IQ: 0.988490661435, symmetry: D₂
face tanget points: minvol.264.txt polyhedron: minvol.264.off

minimum volume polyhedron for n=265

found in 2016 with constrained search by W. R. Deeter
volume: 4.237384687029, IQ: 0.988531963503, symmetry: C₂
face tanget points: minvol.265.txt polyhedron: minvol.265.off

minimum volume polyhedron for n=266

found in 2016 with constrained search by W. R. Deeter
volume: 4.237197438441, IQ: 0.988575648325, symmetry: D₃
face tanget points: minvol.266.txt polyhedron: minvol.266.off

minimum volume polyhedron for n=267

found in 2016 with constrained search by W. R. Deeter
volume: 4.237013711422, IQ: 0.988618515322, symmetry: C₂
face tanget points: minvol.267.txt polyhedron: minvol.267.off

minimum volume polyhedron for n=268

found in 2016 with constrained search by W. R. Deeter
volume: 4.236829196740, IQ: 0.988661569839, symmetry: C₂
face tanget points: minvol.268.txt polyhedron: minvol.268.off

minimum volume polyhedron for n=269

found in 2016 with constrained search by W. R. Deeter
volume: 4.236647451597, IQ: 0.988703981779, symmetry: C₁
face tanget points: minvol.269.txt polyhedron: minvol.269.off

minimum volume polyhedron for n=270

found in 2016 with constrained search by W. R. Deeter
volume: 4.236461839623, IQ: 0.988747299836, symmetry: C₁
face tanget points: minvol.270.txt polyhedron: minvol.270.off

minimum volume polyhedron for n=271

found in 2016 with constrained search by W. R. Deeter
volume: 4.236275586835, IQ: 0.988790771262, symmetry: C_s
face tanget points: minvol.271.txt polyhedron: minvol.271.off

minimum volume polyhedron for n=272

found in 2016 with constrained search by W. R. Deeter
volume: 4.236088810808, IQ: 0.988834368651, symmetry: I_h
face tanget points: minvol.272.txt polyhedron: minvol.272.off

minimum volume polyhedron for n=273

found in 2016 with constrained search by W. R. Deeter
volume: 4.235934771494, IQ: 0.988870327507, symmetry: D₃
face tanget points: minvol.273.txt polyhedron: minvol.273.off

minimum volume polyhedron for n=274

found in 2016 with constrained search by W. R. Deeter
volume: 4.235761184564, IQ: 0.988910852683, symmetry: D₂
face tanget points: minvol.274.txt polyhedron: minvol.274.off

minimum volume polyhedron for n=275

found in 2016 with constrained search by W. R. Deeter
volume: 4.235592533729, IQ: 0.988950228670, symmetry: C₁
face tanget points: minvol.275.txt polyhedron: minvol.275.off

minimum volume polyhedron for n=276

found in 2016 with constrained search by W. R. Deeter
volume: 4.235418709117, IQ: 0.988990815895, symmetry: T
face tanget points: minvol.276.txt polyhedron: minvol.276.off

minimum volume polyhedron for n=277

found in 2016 with constrained search by W. R. Deeter
volume: 4.235249466776, IQ: 0.989030336382, symmetry: C₁
face tanget points: minvol.277.txt polyhedron: minvol.277.off

minimum volume polyhedron for n=278

found in 2016 with constrained search by W. R. Deeter
volume: 4.235081595308, IQ: 0.989069539871, symmetry: C₂
face tanget points: minvol.278.txt polyhedron: minvol.278.off

minimum volume polyhedron for n=279

found in 2016 with constrained search by W. R. Deeter
volume: 4.234909688761, IQ: 0.989109688904, symmetry: C₃
face tanget points: minvol.279.txt polyhedron: minvol.279.off

minimum volume polyhedron for n=280

found in 2016 with constrained search by W. R. Deeter
volume: 4.234742639527, IQ: 0.989148706627, symmetry: C₂
face tanget points: minvol.280.txt polyhedron: minvol.280.off

minimum volume polyhedron for n=281

found in 2016 with constrained search by W. R. Deeter
volume: 4.234570463431, IQ: 0.989188925054, symmetry: C₁
face tanget points: minvol.281.txt polyhedron: minvol.281.off

minimum volume polyhedron for n=282

found in 2016 with constrained search by W. R. Deeter
volume: 4.234397539403, IQ: 0.989229321481, symmetry: I
face tanget points: minvol.282.txt polyhedron: minvol.282.off

minimum volume polyhedron for n=283

found in 2016 with constrained search by W. R. Deeter
volume: 4.234246611508, IQ: 0.989264582134, symmetry: C₃
face tanget points: minvol.283.txt polyhedron: minvol.283.off

minimum volume polyhedron for n=284

found in 2016 with constrained search by W. R. Deeter
volume: 4.234092006440, IQ: 0.989300704476, symmetry: C₂
face tanget points: minvol.284.txt polyhedron: minvol.284.off

minimum volume polyhedron for n=285

found in 2016 with constrained search by W. R. Deeter
volume: 4.233932447370, IQ: 0.989337987050, symmetry: C₁
face tanget points: minvol.285.txt polyhedron: minvol.285.off

minimum volume polyhedron for n=286

found in 2016 with constrained search by W. R. Deeter
volume: 4.233769035096, IQ: 0.989376172877, symmetry: C₂
face tanget points: minvol.286.txt polyhedron: minvol.286.off

minimum volume polyhedron for n=287

found in 2016 with constrained search by W. R. Deeter
volume: 4.233607743314, IQ: 0.989413866082, symmetry: D₅
face tanget points: minvol.287.txt polyhedron: minvol.287.off

minimum volume polyhedron for n=288

found in 2016 with constrained search by W. R. Deeter
volume: 4.233451019080, IQ: 0.989450494622, symmetry: C₂
face tanget points: minvol.288.txt polyhedron: minvol.288.off

minimum volume polyhedron for n=289

found in 2016 with constrained search by W. R. Deeter
volume: 4.233295112335, IQ: 0.989486934795, symmetry: C₂
face tanget points: minvol.289.txt polyhedron: minvol.289.off

minimum volume polyhedron for n=290

found in 2016 with constrained search by W. R. Deeter
volume: 4.233137064890, IQ: 0.989523878055, symmetry: C₁
face tanget points: minvol.290.txt polyhedron: minvol.290.off

minimum volume polyhedron for n=291

found in 2016 with constrained search by W. R. Deeter
volume: 4.232977524525, IQ: 0.989561173079, symmetry: D₃
face tanget points: minvol.291.txt polyhedron: minvol.291.off

minimum volume polyhedron for n=292

found in 2016 with constrained search by W. R. Deeter
volume: 4.232822902553, IQ: 0.989597321036, symmetry: T
face tanget points: minvol.292.txt polyhedron: minvol.292.off

minimum volume polyhedron for n=293

found in 2016 with constrained search by W. R. Deeter
volume: 4.232671169817, IQ: 0.989632796107, symmetry: D₃
face tanget points: minvol.293.txt polyhedron: minvol.293.off

minimum volume polyhedron for n=294

found in 2016 with constrained search by W. R. Deeter
volume: 4.232526769204, IQ: 0.989666559291, symmetry: C₂
face tanget points: minvol.294.txt polyhedron: minvol.294.off

minimum volume polyhedron for n=295

found in 2016 with constrained search by W. R. Deeter
volume: 4.232381674428, IQ: 0.989700487103, symmetry: C₂
face tanget points: minvol.295.txt polyhedron: minvol.295.off

minimum volume polyhedron for n=296

found in 2016 with constrained search by W. R. Deeter
volume: 4.232235993217, IQ: 0.989734554382, symmetry: C₁
face tanget points: minvol.296.txt polyhedron: minvol.296.off

minimum volume polyhedron for n=297

found in 2016 with constrained search by W. R. Deeter
volume: 4.232087262800, IQ: 0.989769337132, symmetry: C₂
face tanget points: minvol.297.txt polyhedron: minvol.297.off

minimum volume polyhedron for n=298

found in 2016 with constrained search by W. R. Deeter
volume: 4.231940398386, IQ: 0.989803685889, symmetry: C₂
face tanget points: minvol.298.txt polyhedron: minvol.298.off

minimum volume polyhedron for n=299

found in 2016 with constrained search by W. R. Deeter
volume: 4.231794353505, IQ: 0.989837845338, symmetry: C₂
face tanget points: minvol.299.txt polyhedron: minvol.299.off

minimum volume polyhedron for n=300

found in 2016 with constrained search by W. R. Deeter
volume: 4.231651358823, IQ: 0.989871293639, symmetry: C₂
face tanget points: minvol.300.txt polyhedron: minvol.300.off

minimum volume polyhedron for n=301

found in 2016 with constrained search by W. R. Deeter
volume: 4.231506208024, IQ: 0.989905248595, symmetry: C_2v
face tanget points: minvol.301.txt polyhedron: minvol.301.off

minimum volume polyhedron for n=302

found in 2016 with constrained search by W. R. Deeter
volume: 4.231363905506, IQ: 0.989938539518, symmetry: C₁
face tanget points: minvol.302.txt polyhedron: minvol.302.off

minimum volume polyhedron for n=303

found in 2016 with constrained search by W. R. Deeter
volume: 4.231220718646, IQ: 0.989972039588, symmetry: C₁
face tanget points: minvol.303.txt polyhedron: minvol.303.off

minimum volume polyhedron for n=304

found in 2016 with constrained search by W. R. Deeter
volume: 4.231076271621, IQ: 0.990005836785, symmetry: D₂
face tanget points: minvol.304.txt polyhedron: minvol.304.off

minimum volume polyhedron for n=305

found in 2016 with constrained search by W. R. Deeter
volume: 4.230934807247, IQ: 0.990038938348, symmetry: C₂
face tanget points: minvol.305.txt polyhedron: minvol.305.off

minimum volume polyhedron for n=306

found in 2016 with constrained search by W. R. Deeter
volume: 4.230796386622, IQ: 0.990071329840, symmetry: T_h
face tanget points: minvol.306.txt polyhedron: minvol.306.off

minimum volume polyhedron for n=307

found in 2016 with constrained search by W. R. Deeter
volume: 4.230655220854, IQ: 0.990104365900, symmetry: C_s
face tanget points: minvol.307.txt polyhedron: minvol.307.off

minimum volume polyhedron for n=308

found in 2016 with constrained search by W. R. Deeter
volume: 4.230514102105, IQ: 0.990137393160, symmetry: D₂
face tanget points: minvol.308.txt polyhedron: minvol.308.off

minimum volume polyhedron for n=309

found in 2016 with constrained search by W. R. Deeter
volume: 4.230386091681, IQ: 0.990167354470, symmetry: C₃
face tanget points: minvol.309.txt polyhedron: minvol.309.off

minimum volume polyhedron for n=310

found in 2016 with constrained search by W. R. Deeter
volume: 4.230252418864, IQ: 0.990198643019, symmetry: C₂
face tanget points: minvol.310.txt polyhedron: minvol.310.off

minimum volume polyhedron for n=311

found in 2016 with constrained search by W. R. Deeter
volume: 4.230115892417, IQ: 0.990230601553, symmetry: C₂
face tanget points: minvol.311.txt polyhedron: minvol.311.off

minimum volume polyhedron for n=312

found in 2016 with constrained search by W. R. Deeter
volume: 4.229980104014, IQ: 0.990262389369, symmetry: I
face tanget points: minvol.312.txt polyhedron: minvol.312.off

minimum volume polyhedron for n=313

found in 2016 with constrained search by W. R. Deeter
volume: 4.229850838555, IQ: 0.990292652073, symmetry: C₁
face tanget points: minvol.313.txt polyhedron: minvol.313.off

minimum volume polyhedron for n=314

found in 2016 with constrained search by W. R. Deeter
volume: 4.229715822538, IQ: 0.990324263031, symmetry: D₂
face tanget points: minvol.314.txt polyhedron: minvol.314.off

minimum volume polyhedron for n=315

found in 2016 with constrained search by W. R. Deeter
volume: 4.229584989088, IQ: 0.990354896661, symmetry: D₃
face tanget points: minvol.315.txt polyhedron: minvol.315.off

minimum volume polyhedron for n=316

found in 2016 with constrained search by W. R. Deeter
volume: 4.229455253420, IQ: 0.990385275125, symmetry: C₂
face tanget points: minvol.316.txt polyhedron: minvol.316.off

minimum volume polyhedron for n=317

found in 2016 with constrained search by W. R. Deeter
volume: 4.229323134407, IQ: 0.990416213580, symmetry: D₅
face tanget points: minvol.317.txt polyhedron: minvol.317.off

minimum volume polyhedron for n=318

found in 2016 with constrained search by W. R. Deeter
volume: 4.229195741156, IQ: 0.990446047229, symmetry: D₃
face tanget points: minvol.318.txt polyhedron: minvol.318.off

minimum volume polyhedron for n=319

found in 2016 with constrained search by W. R. Deeter
volume: 4.229070689236, IQ: 0.990475334321, symmetry: C₁
face tanget points: minvol.319.txt polyhedron: minvol.319.off

minimum volume polyhedron for n=320

found in 2016 with constrained search by W. R. Deeter
volume: 4.228941359487, IQ: 0.990505625099, symmetry: C₂
face tanget points: minvol.320.txt polyhedron: minvol.320.off

minimum volume polyhedron for n=321

found in 2016 with constrained search by W. R. Deeter
volume: 4.228816213000, IQ: 0.990534937865, symmetry: C₁
face tanget points: minvol.321.txt polyhedron: minvol.321.off

minimum volume polyhedron for n=322

found in 2016 with constrained search by W. R. Deeter
volume: 4.228687882676, IQ: 0.990564998175, symmetry: D₂
face tanget points: minvol.322.txt polyhedron: minvol.322.off

minimum volume polyhedron for n=323

found in 2016 with constrained search by W. R. Deeter
volume: 4.228566947756, IQ: 0.990593327844, symmetry: C₁
face tanget points: minvol.323.txt polyhedron: minvol.323.off

minimum volume polyhedron for n=324

found in 2016 with constrained search by W. R. Deeter
volume: 4.228439697692, IQ: 0.990623138618, symmetry: D₂
face tanget points: minvol.324.txt polyhedron: minvol.324.off

minimum volume polyhedron for n=325

found in 2016 with constrained search by W. R. Deeter
volume: 4.228319163922, IQ: 0.990651377627, symmetry: C₂
face tanget points: minvol.325.txt polyhedron: minvol.325.off

minimum volume polyhedron for n=326

found in 2016 with constrained search by W. R. Deeter
volume: 4.228195152491, IQ: 0.990680433073, symmetry: C₁
face tanget points: minvol.326.txt polyhedron: minvol.326.off

minimum volume polyhedron for n=327

found in 2016 with constrained search by W. R. Deeter
volume: 4.228070831388, IQ: 0.990709562785, symmetry: C₂
face tanget points: minvol.327.txt polyhedron: minvol.327.off

minimum volume polyhedron for n=328

found in 2016 with constrained search by W. R. Deeter
volume: 4.227949227223, IQ: 0.990738057547, symmetry: D₂
face tanget points: minvol.328.txt polyhedron: minvol.328.off

minimum volume polyhedron for n=329

found in 2016 with constrained search by W. R. Deeter
volume: 4.227830720176, IQ: 0.990765828158, symmetry: C₂
face tanget points: minvol.329.txt polyhedron: minvol.329.off

minimum volume polyhedron for n=330

found in 2016 with constrained search by W. R. Deeter
volume: 4.227710913115, IQ: 0.990793904993, symmetry: D₃
face tanget points: minvol.330.txt polyhedron: minvol.330.off

minimum volume polyhedron for n=331

found in 2016 with constrained search by W. R. Deeter
volume: 4.227593341244, IQ: 0.990821459557, symmetry: C₂
face tanget points: minvol.331.txt polyhedron: minvol.331.off

minimum volume polyhedron for n=332

found in 2016 with constrained search by W. R. Deeter
volume: 4.227474635932, IQ: 0.990849281314, symmetry: D₂
face tanget points: minvol.332.txt polyhedron: minvol.332.off

minimum volume polyhedron for n=333

found in 2016 with constrained search by W. R. Deeter
volume: 4.227356952644, IQ: 0.990876865074, symmetry: C₂
face tanget points: minvol.333.txt polyhedron: minvol.333.off

minimum volume polyhedron for n=334

found in 2016 with constrained search by W. R. Deeter
volume: 4.227243614235, IQ: 0.990903431891, symmetry: C₂
face tanget points: minvol.334.txt polyhedron: minvol.334.off

minimum volume polyhedron for n=335

found in 2016 with constrained search by W. R. Deeter
volume: 4.227129856553, IQ: 0.990930098419, symmetry: C₁
face tanget points: minvol.335.txt polyhedron: minvol.335.off

minimum volume polyhedron for n=336

found in 2016 with constrained search by W. R. Deeter
volume: 4.227016038410, IQ: 0.990956780557, symmetry: D₂
face tanget points: minvol.336.txt polyhedron: minvol.336.off

minimum volume polyhedron for n=337

found in 2016 with constrained search by W. R. Deeter
volume: 4.226901151386, IQ: 0.990983714728, symmetry: C₁
face tanget points: minvol.337.txt polyhedron: minvol.337.off

minimum volume polyhedron for n=338

found in 2016 with constrained search by W. R. Deeter
volume: 4.226785821173, IQ: 0.991010754272, symmetry: C₁
face tanget points: minvol.338.txt polyhedron: minvol.338.off

minimum volume polyhedron for n=339

found in 2016 with constrained search by W. R. Deeter
volume: 4.226671105956, IQ: 0.991037651092, symmetry: D₃
face tanget points: minvol.339.txt polyhedron: minvol.339.off

minimum volume polyhedron for n=340

found in 2016 with constrained search by W. R. Deeter
volume: 4.226561997485, IQ: 0.991063234676, symmetry: C₂
face tanget points: minvol.340.txt polyhedron: minvol.340.off

minimum volume polyhedron for n=341

found in 2016 with constrained search by W. R. Deeter
volume: 4.226449676075, IQ: 0.991089573005, symmetry: C₂
face tanget points: minvol.341.txt polyhedron: minvol.341.off

minimum volume polyhedron for n=342

found in 2016 with constrained search by W. R. Deeter
volume: 4.226337774572, IQ: 0.991115814261, symmetry: C₃
face tanget points: minvol.342.txt polyhedron: minvol.342.off

minimum volume polyhedron for n=343

found in 2016 with constrained search by W. R. Deeter
volume: 4.226226429278, IQ: 0.991141926464, symmetry: C₁
face tanget points: minvol.343.txt polyhedron: minvol.343.off

minimum volume polyhedron for n=344

found in 2016 with constrained search by W. R. Deeter
volume: 4.226114518726, IQ: 0.991168172615, symmetry: D₂
face tanget points: minvol.344.txt polyhedron: minvol.344.off

minimum volume polyhedron for n=345

found in 2016 with constrained search by W. R. Deeter
volume: 4.226006368958, IQ: 0.991193538078, symmetry: C₁
face tanget points: minvol.345.txt polyhedron: minvol.345.off

minimum volume polyhedron for n=346

found in 2016 with constrained search by W. R. Deeter
volume: 4.225896025919, IQ: 0.991219419289, symmetry: C₁
face tanget points: minvol.346.txt polyhedron: minvol.346.off

minimum volume polyhedron for n=347

found in 2016 with constrained search by W. R. Deeter
volume: 4.225786107665, IQ: 0.991245202210, symmetry: C_s
face tanget points: minvol.347.txt polyhedron: minvol.347.off

minimum volume polyhedron for n=348

found in 2016 with constrained search by W. R. Deeter
volume: 4.225676728150, IQ: 0.991270860093, symmetry: T_h
face tanget points: minvol.348.txt polyhedron: minvol.348.off

minimum volume polyhedron for n=349

found in 2016 with constrained search by W. R. Deeter
volume: 4.225575252232, IQ: 0.991294665164, symmetry: C₁
face tanget points: minvol.349.txt polyhedron: minvol.349.off

minimum volume polyhedron for n=350

found in 2016 with constrained search by W. R. Deeter
volume: 4.225469626556, IQ: 0.991319444935, symmetry: C₂
face tanget points: minvol.350.txt polyhedron: minvol.350.off

minimum volume polyhedron for n=351

found in 2016 with constrained search by W. R. Deeter
volume: 4.225365920428, IQ: 0.991343775585, symmetry: C₁
face tanget points: minvol.351.txt polyhedron: minvol.351.off

minimum volume polyhedron for n=352

found in 2016 with constrained search by W. R. Deeter
volume: 4.225259599249, IQ: 0.991368720997, symmetry: D₅
face tanget points: minvol.352.txt polyhedron: minvol.352.off

minimum volume polyhedron for n=353

found in 2016 with constrained search by W. R. Deeter
volume: 4.225155874933, IQ: 0.991393058334, symmetry: C₃
face tanget points: minvol.353.txt polyhedron: minvol.353.off

minimum volume polyhedron for n=354

found in 2016 with constrained search by W. R. Deeter
volume: 4.225051187605, IQ: 0.991417622839, symmetry: C₁
face tanget points: minvol.354.txt polyhedron: minvol.354.off

minimum volume polyhedron for n=355

found in 2016 with constrained search by W. R. Deeter
volume: 4.224946596967, IQ: 0.991442165871, symmetry: C₁
face tanget points: minvol.355.txt polyhedron: minvol.355.off

minimum volume polyhedron for n=356

found in 2016 with constrained search by W. R. Deeter
volume: 4.224842112378, IQ: 0.991466685232, symmetry: D₃
face tanget points: minvol.356.txt polyhedron: minvol.356.off

minimum volume polyhedron for n=357

found in 2016 with constrained search by W. R. Deeter
volume: 4.224740269689, IQ: 0.991490585786, symmetry: D₅
face tanget points: minvol.357.txt polyhedron: minvol.357.off

minimum volume polyhedron for n=358

found in 2016 with constrained search by W. R. Deeter
volume: 4.224639728034, IQ: 0.991514182142, symmetry: T
face tanget points: minvol.358.txt polyhedron: minvol.358.off

minimum volume polyhedron for n=359

found in 2016 with constrained search by W. R. Deeter
volume: 4.224542984710, IQ: 0.991536888119, symmetry: C₁
face tanget points: minvol.359.txt polyhedron: minvol.359.off

minimum volume polyhedron for n=360

found in 2016 with constrained search by W. R. Deeter
volume: 4.224441557533, IQ: 0.991560694529, symmetry: D₃
face tanget points: minvol.360.txt polyhedron: minvol.360.off

minimum volume polyhedron for n=361

found in 2016 with constrained search by W. R. Deeter
volume: 4.224344732272, IQ: 0.991583421870, symmetry: C₁
face tanget points: minvol.361.txt polyhedron: minvol.361.off

minimum volume polyhedron for n=362

found in 2016 with constrained search by W. R. Deeter
volume: 4.224244849703, IQ: 0.991606867931, symmetry: C₅
face tanget points: minvol.362.txt polyhedron: minvol.362.off

minimum volume polyhedron for n=363

found in 2016 with constrained search by W. R. Deeter
volume: 4.224145555146, IQ: 0.991630177062, symmetry: C₁
face tanget points: minvol.363.txt polyhedron: minvol.363.off

minimum volume polyhedron for n=364

found in 2016 with constrained search by W. R. Deeter
volume: 4.224046214990, IQ: 0.991653497995, symmetry: C₁
face tanget points: minvol.364.txt polyhedron: minvol.364.off

minimum volume polyhedron for n=365

found in 2016 with constrained search by W. R. Deeter
volume: 4.223947424380, IQ: 0.991676691005, symmetry: C₁
face tanget points: minvol.365.txt polyhedron: minvol.365.off

minimum volume polyhedron for n=366

found in 2016 with constrained search by W. R. Deeter
volume: 4.223849181764, IQ: 0.991699756438, symmetry: C₁
face tanget points: minvol.366.txt polyhedron: minvol.366.off

minimum volume polyhedron for n=367

found in 2016 with constrained search by W. R. Deeter
volume: 4.223750899754, IQ: 0.991722832194, symmetry: D₅
face tanget points: minvol.367.txt polyhedron: minvol.367.off

minimum volume polyhedron for n=368

found in 2016 with constrained search by W. R. Deeter
volume: 4.223657854306, IQ: 0.991744679441, symmetry: C₁
face tanget points: minvol.368.txt polyhedron: minvol.368.off

minimum volume polyhedron for n=369

found in 2016 with constrained search by W. R. Deeter
volume: 4.223560648692, IQ: 0.991767504530, symmetry: C₁
face tanget points: minvol.369.txt polyhedron: minvol.369.off

minimum volume polyhedron for n=370

found in 2016 with constrained search by W. R. Deeter
volume: 4.223463870599, IQ: 0.991790230277, symmetry: C₁
face tanget points: minvol.370.txt polyhedron: minvol.370.off

minimum volume polyhedron for n=371

found in 2016 with constrained search by W. R. Deeter
volume: 4.223367550207, IQ: 0.991812849578, symmetry: C₁
face tanget points: minvol.371.txt polyhedron: minvol.371.off

minimum volume polyhedron for n=372

found in 2016 with constrained search by W. R. Deeter
volume: 4.223271041762, IQ: 0.991835514075, symmetry: I
face tanget points: minvol.372.txt polyhedron: minvol.372.off

minimum volume polyhedron for n=373

found in 2016 with constrained search by W. R. Deeter
volume: 4.223188617029, IQ: 0.991854871908, symmetry: C₂
face tanget points: minvol.373.txt polyhedron: minvol.373.off

minimum volume polyhedron for n=374

found in 2016 with constrained search by W. R. Deeter
volume: 4.223094903509, IQ: 0.991876881883, symmetry: C₁
face tanget points: minvol.374.txt polyhedron: minvol.374.off

minimum volume polyhedron for n=375

found in 2016 with constrained search by W. R. Deeter
volume: 4.223001857361, IQ: 0.991898736081, symmetry: C₂
face tanget points: minvol.375.txt polyhedron: minvol.375.off

minimum volume polyhedron for n=376

found in 2016 with constrained search by W. R. Deeter
volume: 4.222909631554, IQ: 0.991920398553, symmetry: C₁
face tanget points: minvol.376.txt polyhedron: minvol.376.off

minimum volume polyhedron for n=377

found in 2016 with constrained search by W. R. Deeter
volume: 4.222817522009, IQ: 0.991942034662, symmetry: D₅
face tanget points: minvol.377.txt polyhedron: minvol.377.off

minimum volume polyhedron for n=378

found in 2021 with constrained search by W. R. Deeter
volume: 4.222731628763, IQ: 0.991962211440, symmetry: C₂
face tanget points: minvol.378.txt polyhedron: minvol.378.off

minimum volume polyhedron for n=379

found in 2021 with constrained search by W. R. Deeter
volume: 4.222640828699, IQ: 0.991983541748, symmetry: C₁
face tanget points: minvol.379.txt polyhedron: minvol.379.off

minimum volume polyhedron for n=380

found in 2021 with constrained search by W. R. Deeter
volume: 4.222550706797, IQ: 0.992004713654, symmetry: C₂
face tanget points: minvol.380.txt polyhedron: minvol.380.off

minimum volume polyhedron for n=381

found in 2016 with constrained search by W. R. Deeter
volume: 4.222460679487, IQ: 0.992025864240, symmetry: C₁
face tanget points: minvol.381.txt polyhedron: minvol.381.off

minimum volume polyhedron for n=382

found in 2016 with constrained search by W. R. Deeter
volume: 4.222370351143, IQ: 0.992047086455, symmetry: D₅
face tanget points: minvol.382.txt polyhedron: minvol.382.off

minimum volume polyhedron for n=383

found in 2016 with constrained search by W. R. Deeter
volume: 4.222283906232, IQ: 0.992067397127, symmetry: C₁
face tanget points: minvol.383.txt polyhedron: minvol.383.off

minimum volume polyhedron for n=384

found in 2016 with constrained search by W. R. Deeter
volume: 4.222194576643, IQ: 0.992088386442, symmetry: C₂
face tanget points: minvol.384.txt polyhedron: minvol.384.off

minimum volume polyhedron for n=385

found in 2016 with constrained search by W. R. Deeter
volume: 4.222106257367, IQ: 0.992109139242, symmetry: C₁
face tanget points: minvol.385.txt polyhedron: minvol.385.off

minimum volume polyhedron for n=386

found in 2016 with constrained search by W. R. Deeter
volume: 4.222018197148, IQ: 0.992129832035, symmetry: C₁
face tanget points: minvol.386.txt polyhedron: minvol.386.off

minimum volume polyhedron for n=387

found in 2016 with constrained search by W. R. Deeter
volume: 4.221930344760, IQ: 0.992150476851, symmetry: D₅
face tanget points: minvol.387.txt polyhedron: minvol.387.off

minimum volume polyhedron for n=388

found in 2016 with constrained search by W. R. Deeter
volume: 4.221843392460, IQ: 0.992170910998, symmetry: C₂
face tanget points: minvol.388.txt polyhedron: minvol.388.off

minimum volume polyhedron for n=389

found in 2016 with constrained search by W. R. Deeter
volume: 4.221756687171, IQ: 0.992191287934, symmetry: C₁
face tanget points: minvol.389.txt polyhedron: minvol.389.off

minimum volume polyhedron for n=390

found in 2016 with constrained search by W. R. Deeter
volume: 4.221670127666, IQ: 0.992211631443, symmetry: T_h
face tanget points: minvol.390.txt polyhedron: minvol.390.off

minimum volume polyhedron for n=391

found in 2016 with constrained search by W. R. Deeter
volume: 4.221588062872, IQ: 0.992230919361, symmetry: C₁
face tanget points: minvol.391.txt polyhedron: minvol.391.off

minimum volume polyhedron for n=392

found in 2016 with constrained search by W. R. Deeter
volume: 4.221501785918, IQ: 0.992251198083, symmetry: I
face tanget points: minvol.392.txt polyhedron: minvol.392.off

minimum volume polyhedron for n=393

found in 2016 with constrained search by W. R. Deeter
volume: 4.221423414991, IQ: 0.992269619274, symmetry: C₂
face tanget points: minvol.393.txt polyhedron: minvol.393.off

minimum volume polyhedron for n=394

found in 2016 with constrained search by W. R. Deeter
volume: 4.221340045942, IQ: 0.992289216031, symmetry: C₁
face tanget points: minvol.394.txt polyhedron: minvol.394.off

minimum volume polyhedron for n=395

found in 2016 with constrained search by W. R. Deeter
volume: 4.221256362421, IQ: 0.992308887486, symmetry: C₁
face tanget points: minvol.395.txt polyhedron: minvol.395.off

minimum volume polyhedron for n=396

found in 2016 with constrained search by W. R. Deeter
volume: 4.221173042702, IQ: 0.992328474197, symmetry: C₁
face tanget points: minvol.396.txt polyhedron: minvol.396.off

minimum volume polyhedron for n=397

found in 2016 with constrained search by W. R. Deeter
volume: 4.221090249064, IQ: 0.992347938004, symmetry: C₁
face tanget points: minvol.397.txt polyhedron: minvol.397.off

minimum volume polyhedron for n=398

found in 2016 with constrained search by W. R. Deeter
volume: 4.221007629343, IQ: 0.992367361686, symmetry: D₃
face tanget points: minvol.398.txt polyhedron: minvol.398.off

minimum volume polyhedron for n=399

found in 2016 with constrained search by W. R. Deeter
volume: 4.220925783511, IQ: 0.992386604178, symmetry: C₁
face tanget points: minvol.399.txt polyhedron: minvol.399.off

minimum volume polyhedron for n=400

found in 2016 with constrained search by W. R. Deeter
volume: 4.220844004364, IQ: 0.992405831738, symmetry: T
face tanget points: minvol.400.txt polyhedron: minvol.400.off

minimum volume polyhedron for n=401

found in 2016 with constrained search by W. R. Deeter
volume: 4.220763932175, IQ: 0.992424658687, symmetry: C₁
face tanget points: minvol.401.txt polyhedron: minvol.401.off

minimum volume polyhedron for n=402

found in 2016 with constrained search by W. R. Deeter
volume: 4.220683254195, IQ: 0.992443628795, symmetry: D₃
face tanget points: minvol.402.txt polyhedron: minvol.402.off

minimum volume polyhedron for n=403

found in 2016 with constrained search by W. R. Deeter
volume: 4.220606148436, IQ: 0.992461759631, symmetry: C₁
face tanget points: minvol.403.txt polyhedron: minvol.403.off

minimum volume polyhedron for n=404

found in 2016 with constrained search by W. R. Deeter
volume: 4.220527713771, IQ: 0.992480203629, symmetry: C₂
face tanget points: minvol.404.txt polyhedron: minvol.404.off

minimum volume polyhedron for n=405

found in 2016 with constrained search by W. R. Deeter
volume: 4.220448657733, IQ: 0.992498794438, symmetry: C₁
face tanget points: minvol.405.txt polyhedron: minvol.405.off

minimum volume polyhedron for n=406

found in 2016 with constrained search by W. R. Deeter
volume: 4.220369523969, IQ: 0.992517404222, symmetry: C₁
face tanget points: minvol.406.txt polyhedron: minvol.406.off

minimum volume polyhedron for n=407

found in 2016 with constrained search by W. R. Deeter
volume: 4.220290927574, IQ: 0.992535888324, symmetry: C₁
face tanget points: minvol.407.txt polyhedron: minvol.407.off

minimum volume polyhedron for n=408

found in 2016 with constrained search by W. R. Deeter
volume: 4.220212531421, IQ: 0.992554326020, symmetry: C₁
face tanget points: minvol.408.txt polyhedron: minvol.408.off

minimum volume polyhedron for n=409

found in 2016 with constrained search by W. R. Deeter
volume: 4.220134473424, IQ: 0.992572684867, symmetry: C₂
face tanget points: minvol.409.txt polyhedron: minvol.409.off

minimum volume polyhedron for n=410

found in 2016 with constrained search by W. R. Deeter
volume: 4.220057548162, IQ: 0.992590777965, symmetry: C₂
face tanget points: minvol.410.txt polyhedron: minvol.410.off

minimum volume polyhedron for n=411

found in 2016 with constrained search by W. R. Deeter
volume: 4.219980494980, IQ: 0.992608901811, symmetry: C₁
face tanget points: minvol.411.txt polyhedron: minvol.411.off

minimum volume polyhedron for n=412

found in 2016 with constrained search by W. R. Deeter
volume: 4.219903527872, IQ: 0.992627006073, symmetry: D₂
face tanget points: minvol.412.txt polyhedron: minvol.412.off

minimum volume polyhedron for n=413

found in 2016 with constrained search by W. R. Deeter
volume: 4.219828440794, IQ: 0.992644668748, symmetry: C₁
face tanget points: minvol.413.txt polyhedron: minvol.413.off

minimum volume polyhedron for n=414

found in 2016 with constrained search by W. R. Deeter
volume: 4.219752642792, IQ: 0.992662499292, symmetry: C₂
face tanget points: minvol.414.txt polyhedron: minvol.414.off

minimum volume polyhedron for n=415

found in 2016 with constrained search by W. R. Deeter
volume: 4.219677240796, IQ: 0.992680237315, symmetry: C₁
face tanget points: minvol.415.txt polyhedron: minvol.415.off

minimum volume polyhedron for n=416

found in 2016 with constrained search by W. R. Deeter
volume: 4.219601760167, IQ: 0.992697994471, symmetry: D₂
face tanget points: minvol.416.txt polyhedron: minvol.416.off

minimum volume polyhedron for n=417

found in 2016 with constrained search by W. R. Deeter
volume: 4.219530379947, IQ: 0.992714787573, symmetry: C₂
face tanget points: minvol.417.txt polyhedron: minvol.417.off

minimum volume polyhedron for n=418

found in 2022 with constrained search by W. R. Deeter
volume: 4.219456526989, IQ: 0.992732163015, symmetry: T
face tanget points: minvol.418.txt polyhedron: minvol.418.off

minimum volume polyhedron for n=419

found in 2022 with constrained search by W. R. Deeter
volume: 4.219383471671, IQ: 0.992749351394, symmetry: C₁
face tanget points: minvol.419.txt polyhedron: minvol.419.off

minimum volume polyhedron for n=420

found in 2016 with constrained search by W. R. Deeter
volume: 4.219310037674, IQ: 0.992766629469, symmetry: C₁
face tanget points: minvol.420.txt polyhedron: minvol.420.off

minimum volume polyhedron for n=421

found in 2016 with constrained search by W. R. Deeter
volume: 4.219236613249, IQ: 0.992783905893, symmetry: C₂
face tanget points: minvol.421.txt polyhedron: minvol.421.off

minimum volume polyhedron for n=422

found in 2022 with constrained search by W. R. Deeter
volume: 4.219163367240, IQ: 0.992801140934, symmetry: D₃
face tanget points: minvol.422.txt polyhedron: minvol.422.off

minimum volume polyhedron for n=423

found in 2016 with constrained search by W. R. Deeter
volume: 4.219091121781, IQ: 0.992818141130, symmetry: C₁
face tanget points: minvol.423.txt polyhedron: minvol.423.off

minimum volume polyhedron for n=424

found in 2016 with constrained search by W. R. Deeter
volume: 4.219018617544, IQ: 0.992835202805, symmetry: C₁
face tanget points: minvol.424.txt polyhedron: minvol.424.off

minimum volume polyhedron for n=425

found in 2016 with constrained search by W. R. Deeter
volume: 4.218946643117, IQ: 0.992852140385, symmetry: C₁
face tanget points: minvol.425.txt polyhedron: minvol.425.off

minimum volume polyhedron for n=426

found in 2016 with constrained search by W. R. Deeter
volume: 4.218875037759, IQ: 0.992868991685, symmetry: D₂
face tanget points: minvol.426.txt polyhedron: minvol.426.off

minimum volume polyhedron for n=427

found in 2016 with constrained search by W. R. Deeter
volume: 4.218803811956, IQ: 0.992885754231, symmetry: C₁
face tanget points: minvol.427.txt polyhedron: minvol.427.off

minimum volume polyhedron for n=428

found in 2016 with constrained search by W. R. Deeter
volume: 4.218732719029, IQ: 0.992902486070, symmetry: S₆
face tanget points: minvol.428.txt polyhedron: minvol.428.off

minimum volume polyhedron for n=429

found in 2016 with constrained search by W. R. Deeter
volume: 4.218662238987, IQ: 0.992919074221, symmetry: C₁
face tanget points: minvol.429.txt polyhedron: minvol.429.off

minimum volume polyhedron for n=430

found in 2016 with constrained search by W. R. Deeter
volume: 4.218592112660, IQ: 0.992935579673, symmetry: C₂
face tanget points: minvol.430.txt polyhedron: minvol.430.off

minimum volume polyhedron for n=431

found in 2016 with constrained search by W. R. Deeter
volume: 4.218522590826, IQ: 0.992951943388, symmetry: C₁
face tanget points: minvol.431.txt polyhedron: minvol.431.off

minimum volume polyhedron for n=432

found in 2016 with constrained search by W. R. Deeter
volume: 4.218453249529, IQ: 0.992968265146, symmetry: C₂
face tanget points: minvol.432.txt polyhedron: minvol.432.off

minimum volume polyhedron for n=433

found in 2016 with constrained search by W. R. Deeter
volume: 4.218384315072, IQ: 0.992984491674, symmetry: C₁
face tanget points: minvol.433.txt polyhedron: minvol.433.off

minimum volume polyhedron for n=434

found in 2016 with constrained search by W. R. Deeter
volume: 4.218315524299, IQ: 0.993000684908, symmetry: C₂
face tanget points: minvol.434.txt polyhedron: minvol.434.off

minimum volume polyhedron for n=435

found in 2016 with constrained search by W. R. Deeter
volume: 4.218247654870, IQ: 0.993016661777, symmetry: C₁
face tanget points: minvol.435.txt polyhedron: minvol.435.off

minimum volume polyhedron for n=436

found in 2016 with constrained search by W. R. Deeter
volume: 4.218179187859, IQ: 0.993032779841, symmetry: D₂
face tanget points: minvol.436.txt polyhedron: minvol.436.off

minimum volume polyhedron for n=437

found in 2016 with constrained search by W. R. Deeter
volume: 4.218111608408, IQ: 0.993048689474, symmetry: C₁
face tanget points: minvol.437.txt polyhedron: minvol.437.off

minimum volume polyhedron for n=438

found in 2016 with constrained search by W. R. Deeter
volume: 4.218043669467, IQ: 0.993064684254, symmetry: D₃
face tanget points: minvol.438.txt polyhedron: minvol.438.off

minimum volume polyhedron for n=439

found in 2016 with constrained search by W. R. Deeter
volume: 4.217976885049, IQ: 0.993080407727, symmetry: C₁
face tanget points: minvol.439.txt polyhedron: minvol.439.off

minimum volume polyhedron for n=440

found in 2016 with constrained search by W. R. Deeter
volume: 4.217910184871, IQ: 0.993096111864, symmetry: C₂
face tanget points: minvol.440.txt polyhedron: minvol.440.off

minimum volume polyhedron for n=441

found in 2016 with constrained search by W. R. Deeter
volume: 4.217843993966, IQ: 0.993111696587, symmetry: C₁
face tanget points: minvol.441.txt polyhedron: minvol.441.off

minimum volume polyhedron for n=442

found in 2016 with constrained search by W. R. Deeter
volume: 4.217777873909, IQ: 0.993127265117, symmetry: C₂
face tanget points: minvol.442.txt polyhedron: minvol.442.off

minimum volume polyhedron for n=443

found in 2022 with constrained search by W. R. Deeter
volume: 4.217711655922, IQ: 0.993142857194, symmetry: C₁
face tanget points: minvol.443.txt polyhedron: minvol.443.off

minimum volume polyhedron for n=444

found in 2016 with constrained search by W. R. Deeter
volume: 4.217644910397, IQ: 0.993158573985, symmetry: C₂
face tanget points: minvol.444.txt polyhedron: minvol.444.off

minimum volume polyhedron for n=445

found in 2016 with constrained search by W. R. Deeter
volume: 4.217579354184, IQ: 0.993174011209, symmetry: C₁
face tanget points: minvol.445.txt polyhedron: minvol.445.off

minimum volume polyhedron for n=446

found in 2016 with constrained search by W. R. Deeter
volume: 4.217514093153, IQ: 0.993189379399, symmetry: C₁
face tanget points: minvol.446.txt polyhedron: minvol.446.off

minimum volume polyhedron for n=447

found in 2016 with constrained search by W. R. Deeter
volume: 4.217449377093, IQ: 0.993204619725, symmetry: C₁
face tanget points: minvol.447.txt polyhedron: minvol.447.off

minimum volume polyhedron for n=448

found in 2016 with constrained search by W. R. Deeter
volume: 4.217384824440, IQ: 0.993219822036, symmetry: D₂
face tanget points: minvol.448.txt polyhedron: minvol.448.off

minimum volume polyhedron for n=449

found in 2016 with constrained search by W. R. Deeter
volume: 4.217320633840, IQ: 0.993234939543, symmetry: C₁
face tanget points: minvol.449.txt polyhedron: minvol.449.off

minimum volume polyhedron for n=450

found in 2016 with constrained search by W. R. Deeter
volume: 4.217256757850, IQ: 0.993249983414, symmetry: C₁
face tanget points: minvol.450.txt polyhedron: minvol.450.off

minimum volume polyhedron for n=451

found in 2016 with constrained search by W. R. Deeter
volume: 4.217193208642, IQ: 0.993264950774, symmetry: C₁
face tanget points: minvol.451.txt polyhedron: minvol.451.off

minimum volume polyhedron for n=452

found in 2016 with constrained search by W. R. Deeter
volume: 4.217129605204, IQ: 0.993279931358, symmetry: C₂
face tanget points: minvol.452.txt polyhedron: minvol.452.off

minimum volume polyhedron for n=453

found in 2016 with constrained search by W. R. Deeter
volume: 4.217066743846, IQ: 0.993294737604, symmetry: C₁
face tanget points: minvol.453.txt polyhedron: minvol.453.off

minimum volume polyhedron for n=454

found in 2016 with constrained search by W. R. Deeter
volume: 4.217004076674, IQ: 0.993309498551, symmetry: C₁
face tanget points: minvol.454.txt polyhedron: minvol.454.off

minimum volume polyhedron for n=455

found in 2016 with constrained search by W. R. Deeter
volume: 4.216941741297, IQ: 0.993324181780, symmetry: C₁
face tanget points: minvol.455.txt polyhedron: minvol.455.off

minimum volume polyhedron for n=456

found in 2016 with constrained search by W. R. Deeter
volume: 4.216878620357, IQ: 0.993339050492, symmetry: D₃
face tanget points: minvol.456.txt polyhedron: minvol.456.off

minimum volume polyhedron for n=457

found in 2016 with constrained search by W. R. Deeter
volume: 4.216817211948, IQ: 0.993353516230, symmetry: C₁
face tanget points: minvol.457.txt polyhedron: minvol.457.off

minimum volume polyhedron for n=458

found in 2016 with constrained search by W. R. Deeter
volume: 4.216756039039, IQ: 0.993367926910, symmetry: C₂
face tanget points: minvol.458.txt polyhedron: minvol.458.off

minimum volume polyhedron for n=459

found in 2016 with constrained search by W. R. Deeter
volume: 4.216695161575, IQ: 0.993382268407, symmetry: C₁
face tanget points: minvol.459.txt polyhedron: minvol.459.off

minimum volume polyhedron for n=460

found in 2016 with constrained search by W. R. Deeter
volume: 4.216633383620, IQ: 0.993396822465, symmetry: D₂
face tanget points: minvol.460.txt polyhedron: minvol.460.off

minimum volume polyhedron for n=461

found in 2016 with constrained search by W. R. Deeter
volume: 4.216573007695, IQ: 0.993411046635, symmetry: C₁
face tanget points: minvol.461.txt polyhedron: minvol.461.off

minimum volume polyhedron for n=462

found in 2022 with constrained search by W. R. Deeter
volume: 4.216512387015, IQ: 0.993425328877, symmetry: C₂
face tanget points: minvol.462.txt polyhedron: minvol.462.off

minimum volume polyhedron for n=463

found in 2022 with constrained search by W. R. Deeter
volume: 4.216452345529, IQ: 0.993439475066, symmetry: C₁
face tanget points: minvol.463.txt polyhedron: minvol.463.off

minimum volume polyhedron for n=464

found in 2022 with constrained search by W. R. Deeter
volume: 4.216392515767, IQ: 0.993453571773, symmetry: C₂
face tanget points: minvol.464.txt polyhedron: minvol.464.off

minimum volume polyhedron for n=465

found in 2016 with constrained search by W. R. Deeter
volume: 4.216331190924, IQ: 0.993468021156, symmetry: D₃
face tanget points: minvol.465.txt polyhedron: minvol.465.off

minimum volume polyhedron for n=466

found in 2016 with constrained search by W. R. Deeter
volume: 4.216272020646, IQ: 0.993481963278, symmetry: C₁
face tanget points: minvol.466.txt polyhedron: minvol.466.off

minimum volume polyhedron for n=467

found in 2022 with constrained search by W. R. Deeter
volume: 4.216212600977, IQ: 0.993495964557, symmetry: C₁
face tanget points: minvol.467.txt polyhedron: minvol.467.off

minimum volume polyhedron for n=468

found in 2016 with constrained search by W. R. Deeter
volume: 4.216152218346, IQ: 0.993510193147, symmetry: T
face tanget points: minvol.468.txt polyhedron: minvol.468.off

minimum volume polyhedron for n=469

found in 2016 with constrained search by W. R. Deeter
volume: 4.216093764013, IQ: 0.993523967740, symmetry: C₁
face tanget points: minvol.469.txt polyhedron: minvol.469.off

minimum volume polyhedron for n=470

found in 2021 from best known minimum energy configuration by W. R. Deeter
volume: 4.216034575294, IQ: 0.993537929386, symmetry: S₆
face tanget points: minvol.470.txt polyhedron: minvol.470.off

minimum volume polyhedron for n=471

found in 2016 with constrained search by W. R. Deeter
volume: 4.215976295418, IQ: 0.993551650027, symmetry: C₁
face tanget points: minvol.471.txt polyhedron: minvol.471.off

minimum volume polyhedron for n=472

found in 2016 with constrained search by W. R. Deeter
volume: 4.215918074451, IQ: 0.993565370772, symmetry: S₁₀
face tanget points: minvol.472.txt polyhedron: minvol.472.off

minimum volume polyhedron for n=473

found in 2016 with constrained search by W. R. Deeter
volume: 4.215860772739, IQ: 0.993578875249, symmetry: C₁
face tanget points: minvol.473.txt polyhedron: minvol.473.off

minimum volume polyhedron for n=474

found in 2016 with constrained search by W. R. Deeter
volume: 4.215803375745, IQ: 0.993592402550, symmetry: C₂
face tanget points: minvol.474.txt polyhedron: minvol.474.off

minimum volume polyhedron for n=475

found in 2016 with constrained search by W. R. Deeter
volume: 4.215746274473, IQ: 0.993605860521, symmetry: C₁
face tanget points: minvol.475.txt polyhedron: minvol.475.off

minimum volume polyhedron for n=476

found in 2016 with constrained search by W. R. Deeter
volume: 4.215689228022, IQ: 0.993619305935, symmetry: C₁
face tanget points: minvol.476.txt polyhedron: minvol.476.off

minimum volume polyhedron for n=477

found in 2016 with constrained search by W. R. Deeter
volume: 4.215632421026, IQ: 0.993632695274, symmetry: C₅
face tanget points: minvol.477.txt polyhedron: minvol.477.off

minimum volume polyhedron for n=478

found in 2022 with constrained search by W. R. Deeter
volume: 4.215575966738, IQ: 0.993646001836, symmetry: C₁
face tanget points: minvol.478.txt polyhedron: minvol.478.off

minimum volume polyhedron for n=479

found in 2016 with constrained search by W. R. Deeter
volume: 4.215519772540, IQ: 0.993659247449, symmetry: C₁
face tanget points: minvol.479.txt polyhedron: minvol.479.off

minimum volume polyhedron for n=480

found in 2016 with constrained search by W. R. Deeter
volume: 4.215462709974, IQ: 0.993672698106, symmetry: C₂
face tanget points: minvol.480.txt polyhedron: minvol.480.off

minimum volume polyhedron for n=481

found in 2016 with constrained search by W. R. Deeter
volume: 4.215406855523, IQ: 0.993685864343, symmetry: C₁
face tanget points: minvol.481.txt polyhedron: minvol.481.off

minimum volume polyhedron for n=482

found in 2016 with constrained search by W. R. Deeter
volume: 4.215351397209, IQ: 0.993698937545, symmetry: C₂
face tanget points: minvol.482.txt polyhedron: minvol.482.off

minimum volume polyhedron for n=483

found in 2016 with constrained search by W. R. Deeter
volume: 4.215296311392, IQ: 0.993711923280, symmetry: C₁
face tanget points: minvol.483.txt polyhedron: minvol.483.off

minimum volume polyhedron for n=484

found in 2016 with constrained search by W. R. Deeter
volume: 4.215241463154, IQ: 0.993724853345, symmetry: C₂
face tanget points: minvol.484.txt polyhedron: minvol.484.off

minimum volume polyhedron for n=485

found in 2022 with constrained search by W. R. Deeter
volume: 4.215186796047, IQ: 0.993737741044, symmetry: C₂
face tanget points: minvol.485.txt polyhedron: minvol.485.off

minimum volume polyhedron for n=486

found in 2016 with constrained search by W. R. Deeter
volume: 4.215131555917, IQ: 0.993750764174, symmetry: C₁
face tanget points: minvol.486.txt polyhedron: minvol.486.off

minimum volume polyhedron for n=487

found in 2022 with constrained search by W. R. Deeter
volume: 4.215077250875, IQ: 0.993763567184, symmetry: C₂
face tanget points: minvol.487.txt polyhedron: minvol.487.off

minimum volume polyhedron for n=488

found in 2023 with constrained search by W. R. Deeter
volume: 4.215023444034, IQ: 0.993776253063, symmetry: C₂
face tanget points: minvol.488.txt polyhedron: minvol.488.off

minimum volume polyhedron for n=489

found in 2022 with constrained search by W. R. Deeter
volume: 4.214969337543, IQ: 0.993789009916, symmetry: C₂
face tanget points: minvol.489.txt polyhedron: minvol.489.off

minimum volume polyhedron for n=490

found in 2016 with constrained search by W. R. Deeter
volume: 4.214914714447, IQ: 0.993801888904, symmetry: C₂
face tanget points: minvol.490.txt polyhedron: minvol.490.off

minimum volume polyhedron for n=491

found in 2016 with constrained search by W. R. Deeter
volume: 4.214861179965, IQ: 0.993814511543, symmetry: C₂
face tanget points: minvol.491.txt polyhedron: minvol.491.off

minimum volume polyhedron for n=492

found in 2016 with constrained search by W. R. Deeter
volume: 4.214807101002, IQ: 0.993827262887, symmetry: C₂
face tanget points: minvol.492.txt polyhedron: minvol.492.off

minimum volume polyhedron for n=493

found in 2022 with constrained search by W. R. Deeter
volume: 4.214754076149, IQ: 0.993839765999, symmetry: C₂
face tanget points: minvol.493.txt polyhedron: minvol.493.off

minimum volume polyhedron for n=494

found in 2022 with constrained search by W. R. Deeter
volume: 4.214701138905, IQ: 0.993852248768, symmetry: C₁
face tanget points: minvol.494.txt polyhedron: minvol.494.off

minimum volume polyhedron for n=495

found in 2023 with constrained search by W. R. Deeter
volume: 4.214647936448, IQ: 0.993864794390, symmetry: C₂
face tanget points: minvol.495.txt polyhedron: minvol.495.off

minimum volume polyhedron for n=496

found in 2022 with constrained search by W. R. Deeter
volume: 4.214595399037, IQ: 0.993877183499, symmetry: C₃
face tanget points: minvol.496.txt polyhedron: minvol.496.off

minimum volume polyhedron for n=497

found in 2023 with constrained search by W. R. Deeter
volume: 4.214542878650, IQ: 0.993889568903, symmetry: D₃
face tanget points: minvol.497.txt polyhedron: minvol.497.off

minimum volume polyhedron for n=498

found in 2022 with constrained search by W. R. Deeter
volume: 4.214490984408, IQ: 0.993901806952, symmetry: C₁
face tanget points: minvol.498.txt polyhedron: minvol.498.off

minimum volume polyhedron for n=499

found in 2022 with constrained search by W. R. Deeter
volume: 4.214439101871, IQ: 0.993914042541, symmetry: C₂
face tanget points: minvol.499.txt polyhedron: minvol.499.off

minimum volume polyhedron for n=500

found in 2022 with constrained search by W. R. Deeter
volume: 4.214387501075, IQ: 0.993926211986, symmetry: C₂
face tanget points: minvol.500.txt polyhedron: minvol.500.off

minimum volume polyhedron for n=501

found in 2022 with constrained search by W. R. Deeter
volume: 4.214336449142, IQ: 0.993938252281, symmetry: C₁
face tanget points: minvol.501.txt polyhedron: minvol.501.off

Note for 1/18/2021: Added new result for n=185.

Note for 1/22/2021: Corrected symmetry for n=165, was C₁, corrected to C₂.

Note for 1/31/2021: Corrected symmetry identification for n=428 (was C_3h, corrected to S₆) and n=472 (was C_5h, corrected to S₁₀).

Note for 2/2/2021: New result for n=470.

Note for 10/17/2023: new results for n=228, 229, 232, 378, 379, 380, 418, 419, 422, 443, 462, 463, 464, 467, 478, 485, 487, 488, 489. Added results for n=493, 494, 495, 496, 497, 498, 499, 500, 501.

Wayne Deeter - wrd@deetour.net

Last modified: October 17, 2023